<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><div class="t m0 x0 h1 y0 ff1 fs0 fc0 sc0 ls1 ws0">T<span class="_0 blank"></span>emas actuales de F<span class="_1 blank"></span>´<span class="_2 blank"></span>\u0131sica Estad<span class="_1 blank"></span>´<span class="_2 blank"></span>\u0131stica</div><div class="t m0 x1 h2 y1 ff2 fs1 fc0 sc0 ls1 ws1">J. J. T<span class="_3 blank"></span>orres</div><div class="t m0 x2 h2 y2 ff2 fs1 fc0 sc0 ls1 ws2">April 12, 2004</div><div class="t m0 x3 h3 y3 ff3 fs2 fc0 sc0 ls1 ws3">1 Programa</div><div class="t m0 x4 h4 y4 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws4">Mo<span class="_4 blank"> </span>delos de equilibrio de Vidrios de Espines</span></div><div class="t m0 x4 h4 y5 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws5">Difusi´<span class="_5 blank"></span>on de iones magn<span class="_6 blank"></span>´<span class="_7 blank"></span>eticos</span></div><div class="t m0 x4 h4 y6 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws6">Memoria<span class="_8 blank"> </span>aso ciativ<span class="_6 blank"></span>a:<span class="_9 blank"> </span>Mo delo<span class="_8 blank"> </span>de<span class="_8 blank"> </span>Hop\ufb01eld</span></div><div class="t m0 x4 h4 y7 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws7">Redes neuronales<span class="_a blank"> </span>fuera del equilibrio</span></div><div class="t m0 x4 h4 y8 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws8">De<span class="_8 blank"> </span>los<span class="_8 blank"> </span>modelos<span class="_a blank"> </span>Ho dgkin-Huxley<span class="_8 blank"> </span>a<span class="_8 blank"> </span>los<span class="_8 blank"> </span>mo delos<span class="_8 blank"> </span>tip o<span class="_8 blank"> </span>Hop\ufb01eld</span></div><div class="t m0 x5 h5 y9 ff5 fs3 fc0 sc0 ls1">1</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x6 ya w1 h6" alt="" src="https://files.passeidireto.com/114c34d8-79c3-4edb-9279-20b76f8c5573/bg2.png"><div class="t m0 x3 h3 yb ff3 fs2 fc0 sc0 ls1 wsa">2<span class="_b blank"> </span>Mo<span class="_4 blank"> </span>delos de equilibrio de vidrios<span class="_9 blank"> </span>de espines</div><div class="t m0 x3 h7 yc ff6 fs1 fc0 sc0 ls1 wsb">2.1<span class="_c blank"> </span>In<span class="_6 blank"></span>tro ducci´<span class="_d blank"></span>on</div><div class="t m0 x3 h5 yd ff5 fs3 fc0 sc0 ls1 wsc">Ciertos materiales como las soluciones<span class="_a blank"> </span>diluidas<span class="_a blank"> </span>de<span class="_a blank"> </span>impurezas<span class="_a blank"> </span>magn´<span class="_5 blank"></span>eticas<span class="_a blank"> </span>en</div><div class="t m0 x3 h5 ye ff5 fs3 fc0 sc0 ls1 wsd">metales nobles,<span class="_8 blank"> </span>por ejemplo el CuMn, son un caso t<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131pico en el que el estado a</div><div class="t m0 x3 h5 yf ff5 fs3 fc0 sc0 ls1 wse">temp eraturas<span class="_a blank"> </span>ba<span class="_f blank"> </span>jas<span class="_a blank"> </span>di\ufb01ere<span class="_a blank"> </span>del<span class="_a blank"> </span>que<span class="_a blank"> </span>presentan<span class="_a blank"> </span>los<span class="_a blank"> </span>materiales<span class="_a blank"> </span><span class="ff7 wsf">ferr<span class="_6 blank"></span>omagn´<span class="_5 blank"></span>etic<span class="_6 blank"></span>os</span></div><div class="t m0 x3 h5 y10 ff5 fs3 fc0 sc0 ls2">y<span class="ff7 ls1 wsf">antiferr<span class="_6 blank"></span>omagn<span class="_6 blank"></span>´<span class="_5 blank"></span>etic<span class="_6 blank"></span>os<span class="ff5">:</span></span></div><div class="t m0 x4 h4 y11 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws10">No presen<span class="_6 blank"></span>tan correlaciones<span class="_10 blank"> </span>de largo alcance ferromagn<span class="_6 blank"></span>´<span class="_7 blank"></span>eticas (<span class="ff8 ls3">m</span><span class="ff4">\u2261</span></span></div><div class="t m0 x7 h8 y12 ff9 fs4 fc0 sc0 ls1">1</div><div class="t m0 x6 h9 y13 ffa fs4 fc0 sc0 ls4">N<span class="ffb fs5 ls1 ws11 v1">P</span><span class="ffc ls5 v2">x</span><span class="ff8 fs3 ls6 v3">s</span><span class="ls7 v4">x</span><span class="ff5 fs3 ls1 ws12 v3">= 0)<span class="ff8 ls8">,</span><span class="ws13">ni an<span class="_6 blank"></span>tiferromagn<span class="_6 blank"></span>´<span class="_5 blank"></span>eticas<span class="_11 blank"> </span>(<span class="ff8 ls9">M<span class="ffc fs4 lsa v5">K</span><span class="ff4 lsb">\u2261</span></span><span class="ff9 fs4 v6">1</span></span></span></div><div class="t m0 x8 ha y13 ffa fs4 fc0 sc0 ls4">N<span class="ffb fs5 lsc v1">P</span><span class="ffc lsd v2">x</span><span class="ff8 fs3 lse v3">e</span><span class="ffd lsf v7">\u2212</span><span class="ls1 ws14 v7">i<span class="ffc ws15">K<span class="ffd ls10">·</span><span class="ls11">x<span class="ff8 fs3 ls12 v8">m</span><span class="ls13 v9">x</span></span><span class="ff5 fs3 ws12 v8">= 0),</span></span></span></div><div class="t m0 x6 h4 y14 ff5 fs3 fc0 sc0 ls1 ws16">aunque<span class="_a blank"> </span>si<span class="_a blank"> </span>presentan<span class="_a blank"> </span>magnetizaci´<span class="_5 blank"></span>on<span class="_a blank"> </span>esp ont´<span class="_5 blank"></span>anea<span class="_8 blank"> </span>lo cal,<span class="_12 blank"> </span><span class="ff8 ls14">m<span class="ffc fs4 ls15 v5">x</span></span><span class="ff4 ws17">6</span><span class="ws18">=<span class="_8 blank"> </span>0.<span class="_10 blank"> </span>Exper-</span></div><div class="t m0 x6 h5 y15 ff5 fs3 fc0 sc0 ls1 ws19">imen<span class="_6 blank"></span>talmen<span class="_6 blank"></span>te,<span class="_11 blank"> </span>esto se<span class="_13 blank"> </span>mani\ufb01esta en que<span class="_13 blank"> </span>la suceptibilidad<span class="_13 blank"> </span>medida<span class="_13 blank"> </span>es</div><div class="t m0 x6 h5 y16 ff5 fs3 fc0 sc0 ls1 ws1a">menor que la<span class="_8 blank"> </span>que deberia hab<span class="_4 blank"> </span>er cuando <span class="ff8 ls16">m<span class="ffc fs4 ls17 v5">x</span></span><span class="ws1b">= 0.</span></div><div class="t m0 x4 h4 y17 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws1c">En<span class="_12 blank"> </span>exp erimentos<span class="_12 blank"> </span>de<span class="_9 blank"> </span><span class="ff7 ws1d">sc<span class="_6 blank"></span>attering <span class="ff5 ws1e">de neutrones,<span class="_9 blank"> </span>no se observ<span class="_6 blank"></span>an picos de</span></span></span></div><div class="t m0 x6 h5 y18 ff7 fs3 fc0 sc0 ls1 ws1f">Br<span class="_6 blank"></span>agg <span class="ff5 ws20">que indicar<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131an la presencia<span class="_8 blank"> </span>de<span class="_8 blank"> </span>orden<span class="_8 blank"> </span><span class="ff7 wsf">antiferr<span class="_6 blank"></span>omagn´<span class="_5 blank"></span>etic<span class="_6 blank"></span>o<span class="ff5">.</span></span></span></div><div class="t m0 x4 h5 y19 ff5 fs3 fc0 sc0 ls1 ws21">Dic<span class="_6 blank"></span>hos<span class="_9 blank"> </span>materiales<span class="_9 blank"> </span>con<span class="_13 blank"> </span>este<span class="_12 blank"> </span>comp ortamiento<span class="_9 blank"> </span>estra \u02dc<span class="_5 blank"></span>no,<span class="_9 blank"> </span>recib en<span class="_9 blank"> </span>el<span class="_9 blank"> </span>nombre</div><div class="t m0 x3 h5 y1a ff5 fs3 fc0 sc0 ls1 ws22">de <span class="ff7 ws23">vidrios de espines</span><span class="ws24">.<span class="_10 blank"> </span>Desde<span class="_12 blank"> </span>un<span class="_a blank"> </span>punto<span class="_a blank"> </span>de<span class="_12 blank"> </span>vista<span class="_a blank"> </span>microsc´<span class="_5 blank"></span>opico,<span class="_9 blank"> </span>este<span class="_12 blank"> </span>comp or-</span></div><div class="t m0 x3 h5 y1b ff5 fs3 fc0 sc0 ls1 ws25">tamien<span class="_6 blank"></span>to macrosc´<span class="_5 blank"></span>opico puede interpretarse de la siguien<span class="_6 blank"></span>te forma:</div><div class="t m0 x4 h4 y1c ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws26">Sup ongamos<span class="_11 blank"> </span>que<span class="_14 blank"> </span>las<span class="_11 blank"> </span>impurezas<span class="_14 blank"> </span>se<span class="_11 blank"> </span>encuentran<span class="_11 blank"> </span>distribuidas<span class="_14 blank"> </span>espacial-</span></div><div class="t m0 x6 h5 y1d ff5 fs3 fc0 sc0 ls1 ws4">men<span class="_6 blank"></span>te de forma aleatoria en el material.</div><div class="t m0 x4 h4 y1e ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws27">Cada uno de estos espines<span class="_15 blank"> </span>in<span class="_6 blank"></span>teracciona con el resto median<span class="_6 blank"></span>te un t´<span class="_5 blank"></span>ermino</span></div><div class="t m0 x6 h4 y1f ff5 fs3 fc0 sc0 ls1 ws28">de in<span class="_6 blank"></span>tercam<span class="_6 blank"></span>bio <span class="ff8 ls18">J</span><span class="ffc fs4 ws29 v5">xy </span><span class="ff4 ls19">\u2261<span class="ff8 ls1a">J</span></span><span class="ws2a">(<span class="ff8 ls1b">r</span><span class="ffc fs4 ws2b v5">xy </span>)<span class="ff8 ls1c">,</span><span class="ws2c">con <span class="ff8 ls1d">r</span><span class="ffc fs4 ws2d v5">xy </span><span class="ff4 ws2e">\u2261 |<span class="ffe ls1e">x</span><span class="ls1f">\u2212<span class="ffe ls20">y</span></span><span class="ws17">|</span></span><span class="ws2f">.<span class="_9 blank"> </span>Esta interacci´<span class="_5 blank"></span>on tiene</span></span></span></div><div class="t m0 x6 h5 y20 ff5 fs3 fc0 sc0 ls1 ws20">un comp<span class="_4 blank"> </span>ortamiento ondulatorio y decrece con la distancia<span class="_8 blank"> </span>en<span class="_8 blank"> </span>la forma</div><div class="t m0 x9 hb y21 ff8 fs3 fc0 sc0 ls1a">J<span class="ff5 ls1 ws2a">(</span><span class="ls21">r<span class="ffc fs4 ls1 ws30 v5">xy </span><span class="ff5 ls22">)<span class="ff4 ls23">\u221d</span><span class="ls1 ws31 va">cos(2</span></span><span class="ls24 va">k</span><span class="ffa fs4 ls25 vb">F</span><span class="ls26 va">r</span><span class="ffc fs4 ls1 ws2b vb">xy </span><span class="ff5 ls1 va">)</span></span></div><div class="t m0 xa hc y22 ff8 fs3 fc0 sc0 ls27">r<span class="ff9 fs4 ls1 vc">3</span></div><div class="t m0 xb hd y23 ffc fs4 fc0 sc0 ls1">xy</div><div class="t m0 xc h4 y24 ff8 fs3 fc0 sc0 ls1 ws32">, k<span class="ffa fs4 ls25 v5">F</span><span class="ls26">r</span><span class="ffc fs4 ws29 v5">xy </span><span class="ff4 ls28">\ue01d</span><span class="ff5 ws2a">1</span><span class="ls29">.</span><span class="ff5">(1)</span></div><div class="t m0 x4 h4 y25 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws26">Sup oniendo<span class="_8 blank"> </span>que<span class="_16 blank"> </span>las<span class="_16 blank"> </span>impurezas<span class="_8 blank"> </span>magn<span class="_6 blank"></span>´<span class="_7 blank"></span>eticas<span class="_16 blank"> </span>no<span class="_16 blank"> </span>se<span class="_8 blank"> </span>difunden<span class="_16 blank"> </span>p or<span class="_16 blank"> </span>el<span class="_8 blank"> </span>metal,</span></div><div class="t m0 x6 h5 y26 ff5 fs3 fc0 sc0 ls1 ws33">el<span class="_12 blank"> </span>que<span class="_9 blank"> </span>tengamos<span class="_9 blank"> </span>espines<span class="_9 blank"> </span>en<span class="_9 blank"> </span>p osiciones<span class="_9 blank"> </span>aleatorias<span class="_12 blank"> </span>hace<span class="_9 blank"> </span>que<span class="_9 blank"> </span><span class="ff8 ls2a">J</span><span class="ffc fs4 ws34 v5">xy </span>pueda</div><div class="t m0 x6 h5 y27 ff5 fs3 fc0 sc0 ls1 ws35">ser p<span class="_4 blank"> </span>ositiv<span class="_6 blank"></span>a o negativ<span class="_6 blank"></span>a dependiendo<span class="_12 blank"> </span>de su<span class="_12 blank"> </span>p<span class="_4 blank"> </span>osici´<span class="_5 blank"></span>on<span class="_12 blank"> </span>con resp<span class="_4 blank"> </span>ecto<span class="_12 blank"> </span>a las</div><div class="t m0 x6 h5 y28 ff5 fs3 fc0 sc0 ls1 ws36">dem´<span class="_5 blank"></span>as,<span class="_13 blank"> </span>adquiriendo<span class="_13 blank"> </span>el sistema una<span class="_13 blank"> </span>distribuci´<span class="_5 blank"></span>on espacial aleatoria de</div><div class="t m0 x6 h5 y29 ff5 fs3 fc0 sc0 ls1 ws37">in<span class="_6 blank"></span>teracciones<span class="_8 blank"> </span>magn´<span class="_5 blank"></span>eticas<span class="_8 blank"> </span>p ositiv<span class="_6 blank"></span>as<span class="_8 blank"> </span>o<span class="_8 blank"> </span>negativ<span class="_17 blank"></span>as.<span class="_9 blank"> </span>Esto<span class="_8 blank"> </span>prov<span class="_17 blank"></span>o ca<span class="_8 blank"> </span>que<span class="_8 blank"> </span>hay<span class="_17 blank"></span>a</div><div class="t m0 x6 h5 y2a ff5 fs3 fc0 sc0 ls1 ws38">con\ufb01guraciones<span class="_9 blank"> </span>de<span class="_9 blank"> </span>espines<span class="_13 blank"> </span>que<span class="_12 blank"> </span>no<span class="_9 blank"> </span>puedan<span class="_9 blank"> </span>satisfacer<span class="_9 blank"> </span>to das<span class="_9 blank"> </span>las<span class="_9 blank"> </span>in<span class="_6 blank"></span>tera-</div><div class="t m0 x6 h5 y2b ff5 fs3 fc0 sc0 ls1 ws39">ciones y<span class="_17 blank"></span>, p<span class="_4 blank"> </span>or lo tan<span class="_17 blank"></span>to,<span class="_9 blank"> </span>no se consiga el estado de m<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131nima energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a.<span class="_18 blank"> </span>A</div><div class="t m0 x6 h5 y2c ff5 fs3 fc0 sc0 ls1 ws3a">este hecho se le<span class="_8 blank"> </span>llama <span class="ff7 ws3b">frustr<span class="_6 blank"></span>aci´<span class="_5 blank"></span>on est´<span class="_5 blank"></span>atic<span class="_17 blank"></span>a<span class="ff5">.</span></span></div><div class="t m0 x4 h4 y2d ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws3c">La<span class="_a blank"> </span>existencia<span class="_a blank"> </span>de<span class="_12 blank"> </span>estos<span class="_a blank"> </span>dominios<span class="_a blank"> </span>frustrados,<span class="_12 blank"> </span>distribuidos<span class="_12 blank"> </span>al<span class="_a blank"> </span>azar<span class="_a blank"> </span>p or<span class="_a blank"> </span>el</span></div><div class="t m0 x6 h5 y2e ff5 fs3 fc0 sc0 ls1 ws3d">metal, p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>dr<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131a<span class="_16 blank"> </span>explicar<span class="_a blank"> </span>la no presencia<span class="_a blank"> </span>de orden de largo alcance como</div><div class="t m0 x6 h5 y2f ff5 fs3 fc0 sc0 ls1 wse">el<span class="_8 blank"> </span>que<span class="_8 blank"> </span>se<span class="_8 blank"> </span>observ<span class="_17 blank"></span>a<span class="_8 blank"> </span>incluso<span class="_a blank"> </span>a<span class="_8 blank"> </span>temperaturas<span class="_a blank"> </span>m<span class="_6 blank"></span>uy<span class="_8 blank"> </span>ba jas.</div><div class="t m0 x5 h5 y30 ff5 fs3 fc0 sc0 ls1">2</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi xd y31 w2 he" alt="" src="https://files.passeidireto.com/114c34d8-79c3-4edb-9279-20b76f8c5573/bg3.png"><div class="t m0 xe hf y32 fff fs6 fc0 sc0 ls1">0</div><div class="t m0 xf hf y33 fff fs6 fc0 sc0 ls1 ws3e">r<span class="fs7 vd">xy</span></div><div class="t m0 x10 hf y34 fff fs6 fc0 sc0 ls1 ws3e">J(r<span class="fs7 ws3f vd">xy</span>)</div><div class="t m0 x3 h5 y35 ff5 fs3 fc0 sc0 ls1 ws40">Figure 1:<span class="_9 blank"> </span>Interacci´<span class="_5 blank"></span>on de intercam<span class="_17 blank"></span>bio<span class="_a blank"> </span><span class="ff8 ls2b">J</span><span class="ffc fs4 ws41 v5">xy </span><span class="ws20">como funci´<span class="_5 blank"></span>on de<span class="_a blank"> </span>la distancia entre</span></div><div class="t m0 x3 h5 y36 ff5 fs3 fc0 sc0 ls1">espines.</div><div class="c xd y37 w3 h10"><div class="t m0 x11 h11 y38 ff10 fs8 fc0 sc0 ls1">\u2212J</div><div class="t m0 x12 h11 y39 ff10 fs8 fc0 sc0 ls1">+J</div><div class="t m0 x13 h11 y38 ff10 fs8 fc0 sc0 ls1">+J</div><div class="t m0 x3 h11 y3a ff10 fs8 fc0 sc0 ls1">+J</div></div><div class="t m0 x3 h5 y3b ff5 fs3 fc0 sc0 ls1 ws42">Figure 2:<span class="_9 blank"> </span>La \ufb01gura muestra un dominio de<span class="_8 blank"> </span>espines<span class="_8 blank"> </span>frustrado.<span class="_9 blank"> </span>La interacci´<span class="_5 blank"></span>on</div><div class="t m0 x3 h5 y3c ff5 fs3 fc0 sc0 ls1 ws43">de la derec<span class="_6 blank"></span>ha no puede ser satisfecha al ser de tipo antiferromagn<span class="_17 blank"></span>´<span class="_7 blank"></span>etica y estar</div><div class="t m0 x3 h5 y3d ff5 fs3 fc0 sc0 ls1 ws33">los<span class="_8 blank"> </span>dos<span class="_8 blank"> </span>espines<span class="_8 blank"> </span>en<span class="_8 blank"> </span>p osici´<span class="_5 blank"></span>on<span class="_8 blank"> </span>paralela.</div><div class="t m0 x4 h4 y3e ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws44">A parte de soluciones<span class="_15 blank"> </span>met´<span class="_5 blank"></span>alicas con impurezas magn´<span class="_5 blank"></span>eticas,<span class="_15 blank"> </span>existen otros</span></div><div class="t m0 x6 h5 y3f ff5 fs3 fc0 sc0 ls1 ws24">sistemas<span class="_13 blank"> </span>que<span class="_11 blank"> </span>presen<span class="_6 blank"></span>tan<span class="_13 blank"> </span>comp ortamiento<span class="_13 blank"> </span><span class="ff7 ws45">vidrio de espines</span><span class="ws46">,<span class="_11 blank"> </span>como las</span></div><div class="t m0 x5 h5 y30 ff5 fs3 fc0 sc0 ls1">3</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><div class="t m0 x6 h5 yb ff5 fs3 fc0 sc0 ls1 ws47">mezclas<span class="_8 blank"> </span>ferro el<span class="_6 blank"></span>´<span class="_7 blank"></span>ectricas-an<span class="_6 blank"></span>tiferro el<span class="_6 blank"></span>´<span class="_7 blank"></span>ectricas,<span class="_8 blank"> </span>en<span class="_8 blank"> </span>las<span class="_16 blank"> </span>que<span class="_8 blank"> </span>el<span class="_8 blank"> </span>momen<span class="_17 blank"></span>to<span class="_8 blank"> </span>dip o-</div><div class="t m0 x6 h5 y40 ff5 fs3 fc0 sc0 ls1 ws48">lar el<span class="_17 blank"></span>´<span class="_7 blank"></span>ectrico<span class="_15 blank"> </span>har<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a el papel de esp<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131n, y ciertos cristales<span class="_15 blank"> </span>moleculares desor-</div><div class="t m0 x6 h5 y41 ff5 fs3 fc0 sc0 ls1 ws49">denados, en los que el pap<span class="_4 blank"> </span>el del esp<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131n lo har<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a<span class="_15 blank"> </span>el momento cuadrupolar</div><div class="t m0 x6 h5 y42 ff5 fs3 fc0 sc0 ls1 ws2a">el<span class="_6 blank"></span>´<span class="_7 blank"></span>ectrico.</div><div class="t m0 x5 h5 y30 ff5 fs3 fc0 sc0 ls1">4</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x14 y43 w4 h12" alt="" src="https://files.passeidireto.com/114c34d8-79c3-4edb-9279-20b76f8c5573/bg5.png"><div class="t m0 x3 h7 yb ff6 fs1 fc0 sc0 ls1 ws4a">2.2<span class="_c blank"> </span>In<span class="_17 blank"></span>teracci´<span class="_19 blank"></span>on RKKY</div><div class="t m0 x4 h4 y44 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws4b">En una mezcla<span class="_8 blank"> </span>de impurezas met´<span class="_5 blank"></span>alicas con metales nobles (CuMn)<span class="_8 blank"> </span>la</span></div><div class="t m0 x6 h5 y45 ff5 fs3 fc0 sc0 ls1 ws4c">in<span class="_6 blank"></span>teracci´<span class="_5 blank"></span>on entre los momen<span class="_17 blank"></span>tos<span class="_9 blank"> </span>magn´<span class="_5 blank"></span>eticos de las impurezas<span class="_9 blank"> </span>(Mn) se</div><div class="t m0 x6 h5 y46 ff5 fs3 fc0 sc0 ls1 ws33">pro duce<span class="_13 blank"> </span>p orque<span class="_11 blank"> </span>cada<span class="_13 blank"> </span>una<span class="_13 blank"> </span>de<span class="_13 blank"> </span>ellas<span class="_13 blank"> </span>p olariza<span class="_13 blank"> </span>el<span class="_13 blank"> </span>niv<span class="_6 blank"></span>el<span class="_11 blank"> </span>de<span class="_13 blank"> </span>F<span class="_3 blank"></span>ermi<span class="_13 blank"> </span>de<span class="_11 blank"> </span>los</div><div class="t m0 x6 h5 y47 ff5 fs3 fc0 sc0 ls1 ws4d">electrones de conducci´<span class="_5 blank"></span>on<span class="_a blank"> </span>del metal (Cu).</div><div class="t m0 x4 h4 y48 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws4e">En el marco de la teor<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a de apan<span class="_17 blank"></span>tallamiento de <span class="ff7 wsf">Lindhar<span class="_17 blank"></span>d<span class="ff5 ws4f">, [1] para un</span></span></span></div><div class="t m0 x6 h5 y49 ff5 fs3 fc0 sc0 ls1 ws33">esp<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131n<span class="_8 blank"> </span>sencillo,<span class="_8 blank"> </span>dicha<span class="_8 blank"> </span>p olarizaci´<span class="_5 blank"></span>on<span class="_8 blank"> </span>v<span class="_17 blank"></span>ar<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a<span class="_8 blank"> </span>en<span class="_8 blank"> </span>la<span class="_8 blank"> </span>forma:</div><div class="t m0 x15 h13 y4a ff8 fs3 fc0 sc0 ls2c"><<span class="ffe ls2d">s<span class="ffc fs4 ls2e v5">x</span><span class="ff5 ls1 ws2a">(</span><span class="ls1 ws50">r<span class="ff5 ls2f">)</span></span></span><span class="ls1 ws51">><span class="ff5 ls30">=</span><span class="ffb fs5 ve">X</span></span></div><div class="t m0 x16 hd y4b ffc fs4 fc0 sc0 ls1">q</div><div class="t m0 x17 h14 y4a ff8 fs3 fc0 sc0 ls31">\u03c7<span class="ff9 fs4 ls32 v5">0</span><span class="ff5 ls1 ws2a">(<span class="ffe ws50">q</span>)</span><span class="ls33">e<span class="ffa fs4 ls1 ws14 vf">i<span class="ffc ws15">q<span class="ffd ws52">·<span class="ff9 ws53">(</span></span>r<span class="ffd ws52">\u2212</span>x<span class="ff9 ls34">)</span></span></span><span class="ffe ls26">s<span class="ffc fs4 ls35 v5">x</span><span class="ff5 ls1">(2)</span></span></span></div><div class="t m0 x6 h5 y4c ff5 fs3 fc0 sc0 ls1 ws4">alrededor de las impureza en <span class="ffe ws50">x</span>.</div><div class="t m0 x4 h4 y4d ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff8 ls36">\u03c7<span class="ff9 fs4 ls37 v5">0</span><span class="ff5 ls1 ws2a">(<span class="ffe ws50">q</span><span class="ws54">) es la suceptibilidad<span class="_11 blank"> </span>(</span></span><span class="ls1 ws55">\u2202 m<span class="_4 blank"> </span><span class="ffc fs4 ls38 v5">x</span><span class="ws56">/\u2202 h<span class="ffc fs4 ls39 v5">x</span><span class="ff5 ws57">) del gas de electrones<span class="_14 blank"> </span>de con-</span></span></span></span></div><div class="t m0 x6 h5 y4e ff5 fs3 fc0 sc0 ls1 ws2a">ducci´<span class="_5 blank"></span>on,</div><div class="t m0 x18 h15 y4f ff8 fs3 fc0 sc0 ls31">\u03c7<span class="ff9 fs4 ls37 v5">0</span><span class="ff5 ls1 ws2a">(<span class="ffe ws50">q</span><span class="ws1b">) = <span class="ff4 ls3a">\u2212</span><span class="va">1</span></span></span></div><div class="t m0 x19 h16 y50 ff8 fs3 fc0 sc0 ls3b">N<span class="ffb fs5 ls1 v10">X</span></div><div class="t m0 xf hd y51 ffc fs4 fc0 sc0 ls1">k</div><div class="t m0 x1a h4 y52 ff8 fs3 fc0 sc0 ls3c">f<span class="ffc fs4 ls3d v5">k</span><span class="ff4 ls3e">\u2212</span><span class="ls3f">f<span class="ffc fs4 ls1 ws15 v5">k<span class="ff9 ws53">+<span class="ffc">q</span></span></span></span></div><div class="t m0 x1b h4 y50 ff8 fs3 fc0 sc0 ls40">\ue00f<span class="ffc fs4 ls3d v5">k</span><span class="ff4 ls3e">\u2212</span><span class="ls41">\ue00f<span class="ffc fs4 ls1 ws15 v5">k<span class="ff9 ws53">+<span class="ffc">q</span></span></span></span></div><div class="t m0 x1c h5 y4f ff5 fs3 fc0 sc0 ls1">(3)</div><div class="t m0 x6 h5 y53 ff5 fs3 fc0 sc0 ls1">donde</div><div class="t m0 x2 h17 y54 ff8 fs3 fc0 sc0 ls3c">f<span class="ffc fs4 ls17 v5">k</span><span class="ff5 ls42">=<span class="ls1 va">1</span></span></div><div class="t m0 x1d h18 y55 ff5 fs3 fc0 sc0 ls1 ws58">1 + <span class="ff8 ls43">e<span class="ls44 vb">\u03b2</span></span><span class="ls45 vb">(</span><span class="ff9 fs4 ws53 v11">¯<span class="_e blank"></span><span class="ffa">h</span></span></div><div class="t m0 x1e h19 y56 ff11 fs9 fc0 sc0 ls46">2<span class="ffa fs4 ls47 v12">k</span><span class="ls1 v0">2</span></div><div class="t m0 xc h1a y57 ff9 fs4 fc0 sc0 ls1 ws53">2<span class="ffa ls48">m<span class="ff12 fs9 ls49 v13">e</span><span class="ff4 fs3 ls4a v3">\u2212<span class="ff8 ls1 ws51">µ<span class="ff5 ls4b">)</span><span class="ls4c ve">,</span><span class="ff5 ve">(4)</span></span></span></span></div><div class="t m0 x6 h5 y58 ff5 fs3 fc0 sc0 ls1 ws59">es la funci´<span class="_5 blank"></span>on de F<span class="_17 blank"></span>ermi y <span class="ff8 ls4d">\ue00f<span class="ffc fs4 ls4e v5">k</span></span><span class="ws5a">es la energ<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131a de banda de un electr´<span class="_5 blank"></span>on de</span></div><div class="t m0 x6 h5 y59 ff5 fs3 fc0 sc0 ls1 ws5b">momen<span class="_6 blank"></span>to <span class="ffe ws50">k</span>.</div><div class="t m0 x4 h4 y5a ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws5c">En aproximaci´<span class="_5 blank"></span>on de electrones<span class="_8 blank"> </span>libres,<span class="_a blank"> </span>se tiene<span class="_8 blank"> </span>para (<span class="ff8 ls4f">r</span><span class="ff4 ws5d">\u2192 \u221e</span>):</span></div><div class="t m0 x1 h1b y5b ff8 fs3 fc0 sc0 ls31">\u03c7<span class="ff9 fs4 ls37 v5">0</span><span class="ff5 ls1 ws2a">(</span><span class="ls50">r<span class="ff5 ls22">)<span class="ff4 ls51">\u221d</span><span class="ls1 ws31 va">cos(2</span></span><span class="ls24 va">k</span><span class="ffa fs4 ls52 vb">F</span><span class="va">r<span class="ff5 ls1">)</span></span></span></div><div class="t m0 x1f h1c y5c ff8 fs3 fc0 sc0 ls53">r<span class="ff9 fs4 ls54 v3">3</span><span class="ls55 va">,<span class="ff5 ls1">(5)</span></span></div><div class="t m0 x6 h5 y5d ff5 fs3 fc0 sc0 ls1 ws5e">donde <span class="ff8 ls56">\u03c7<span class="ff9 fs4 ls37 v5">0</span></span><span class="ws2a">(<span class="ff8 ls50">r</span><span class="ws4">) es la transformada de F<span class="_3 blank"></span>ourier de <span class="ff8 ls57">\u03c7<span class="ff9 fs4 ls32 v5">0</span></span><span class="ws2a">(<span class="ff8 ls58">q</span>).</span></span></span></div><div class="t m0 x4 h4 y5e ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws5f">De forma efectiv<span class="_17 blank"></span>a,<span class="_a blank"> </span>la interacci´<span class="_5 blank"></span>on entre momen<span class="_17 blank"></span>tos<span class="_a blank"> </span>magn´<span class="_5 blank"></span>eticos<span class="_a blank"> </span>de<span class="_a blank"> </span>esp<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131n</span></div><div class="t m0 x6 h5 y5f ff5 fs3 fc0 sc0 ls1 ws33">de<span class="_9 blank"> </span>las<span class="_9 blank"> </span>impurezas<span class="_13 blank"> </span>es<span class="_9 blank"> </span>debida<span class="_9 blank"> </span>a<span class="_9 blank"> </span>esta<span class="_9 blank"> </span>p olarizaci´<span class="_5 blank"></span>on<span class="_9 blank"> </span>y<span class="_13 blank"> </span>posee<span class="_1a blank"> </span>este<span class="_9 blank"> </span>comp or-</div><div class="t m0 x6 h5 y60 ff5 fs3 fc0 sc0 ls1 ws60">tamien<span class="_6 blank"></span>to, es decir,</div><div class="t m0 x9 hb y61 ff8 fs3 fc0 sc0 ls59">J<span class="ffc fs4 ls1 ws15 v5">x<span class="ffa ws14">,<span class="ffc ls5a">y</span></span></span><span class="ff5 ls1 ws2a">(</span><span class="ls50">r<span class="ff5 ls1 ws1b">) = </span><span class="ls5b">J<span class="ff5 ls1 ws31 va">cos(2</span><span class="ls24 va">k</span><span class="ffa fs4 ls25 vb">F</span><span class="ls5c va">r<span class="ff5 ls5d">+<span class="ff8 ls1 ws51">\u03c6<span class="ff5">)</span></span></span></span></span></span></div><div class="t m0 x19 h1d y62 ff8 fs3 fc0 sc0 ls27">r<span class="ff9 fs4 ls5e v3">3</span><span class="ls1 ws61 va">,<span class="_1b blank"> </span>r <span class="ff4 ws62">\u2192 \u221e<span class="ff8 ls5f">.</span><span class="ff5">(6)</span></span></span></div><div class="t m0 x6 h5 y63 ff5 fs3 fc0 sc0 ls1 ws63">Aqu<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131, <span class="ff8 ls60">J</span><span class="ls2">y<span class="ff8 ls61">\u03c6</span></span><span class="ws20">son caracter<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131sticos de la mezcla<span class="_8 blank"> </span>magn´<span class="_5 blank"></span>etica.</span></div><div class="t m0 x4 h4 y64 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws33">Esta<span class="_16 blank"> </span>interaccion<span class="_16 blank"> </span>fue<span class="_16 blank"> </span>estudiada<span class="_8 blank"> </span>p or<span class="_16 blank"> </span><span class="ff7 ws64">Ruderman </span><span class="ls62">y</span><span class="ff7 ws65">Kittel </span><span class="ws3c">(1954)<span class="_15 blank"> </span>[2]<span class="_16 blank"> </span>y<span class="_8 blank"> </span>pos-</span></span></div><div class="t m0 x6 h5 y65 ff5 fs3 fc0 sc0 ls1 ws33">teriormen<span class="_6 blank"></span>te<span class="_12 blank"> </span>p or<span class="_12 blank"> </span><span class="ff7 ws66">Kasuya </span><span class="ws67">(1956) [3] y<span class="_9 blank"> </span><span class="ff7 ws68">Y<span class="_17 blank"></span>osida <span class="ff5 ws69">(1957),<span class="_12 blank"> </span>[4]<span class="_12 blank"> </span>y<span class="_12 blank"> </span>es<span class="_12 blank"> </span>cono cida</span></span></span></div><div class="t m0 x6 h5 y66 ff5 fs3 fc0 sc0 ls1 ws6a">como la interacci´<span class="_5 blank"></span>on RKKY (<span class="ff7 ws6b">vidrios </span>RKKY).</div><div class="t m0 x5 h5 y67 ff5 fs3 fc0 sc0 ls1">5</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><div class="t m0 x4 h4 yb ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws6c">Las oscilaciones de <span class="ff8 ls63">J</span><span class="ffc fs4 ws6d v5">xy </span><span class="ws22">son las resp<span class="_4 blank"> </span>onsables<span class="_9 blank"> </span>de la comp<span class="_4 blank"> </span>etencia de in-</span></span></div><div class="t m0 x6 h5 y40 ff5 fs3 fc0 sc0 ls1 ws6e">teracciones en los <span class="ff7 ws6f">vidrios de espines</span><span class="ws3c">,<span class="_16 blank"> </span>y<span class="_16 blank"> </span>la<span class="_16 blank"> </span>aleatoriedad<span class="_16 blank"> </span>en<span class="_16 blank"> </span>las<span class="_16 blank"> </span>p osiciones</span></div><div class="t m0 x6 h5 y41 ff5 fs3 fc0 sc0 ls1 ws70">de las impurezas da el<span class="_16 blank"> </span>car´<span class="_5 blank"></span>acter de in<span class="_17 blank"></span>teracciones<span class="_8 blank"> </span>aleatorias t<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131pico de los</div><div class="t m0 x6 h5 y42 ff7 fs3 fc0 sc0 ls1 ws71">vidrios de espines<span class="ff5">.</span></div><div class="t m0 x5 h5 y30 ff5 fs3 fc0 sc0 ls1">6</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><div class="t m0 x3 h7 yb ff6 fs1 fc0 sc0 ls1 ws72">2.3<span class="_c blank"> </span>Promedios en sistemas desordenados</div><div class="t m0 x4 h4 y44 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws73">Basados en las dos propiedades anteriores,<span class="_15 blank"> </span>competencia<span class="_15 blank"> </span>de in<span class="_17 blank"></span>teracciones</span></div><div class="t m0 x6 h5 y45 ff5 fs3 fc0 sc0 ls1 ws39">y aleatoriedad de las mismas,<span class="_1a blank"> </span>en la<span class="_9 blank"> </span>´<span class="_5 blank"></span>ultimas d<span class="_17 blank"></span>´<span class="_7 blank"></span>ecadas<span class="_9 blank"> </span>se han desarrol-</div><div class="t m0 x6 h5 y46 ff5 fs3 fc0 sc0 ls1 ws24">lado<span class="_16 blank"> </span>multitud<span class="_16 blank"> </span>de<span class="_8 blank"> </span>modelos<span class="_8 blank"> </span>f<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131sico-matem´<span class="_5 blank"></span>aticos<span class="_16 blank"> </span>para<span class="_8 blank"> </span>en<span class="_17 blank"></span>tender<span class="_8 blank"> </span>el<span class="_8 blank"> </span>compor-</div><div class="t m0 x6 h5 y47 ff5 fs3 fc0 sc0 ls1 ws74">tamien<span class="_6 blank"></span>to <span class="ff7 ws75">vidrio de espin</span>.</div><div class="t m0 x4 h1e y48 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws8">Aqui<span class="_8 blank"> </span>estamos<span class="_a blank"> </span>in<span class="_6 blank"></span>teresados<span class="_8 blank"> </span>en<span class="_a blank"> </span>mo delos<span class="_8 blank"> </span>mec´<span class="_5 blank"></span>anico-estad<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131sticos.<span class="_10 blank"> </span><span class="v14">´</span></span></div><div class="t m0 x20 h5 y48 ff5 fs3 fc0 sc0 ls1 ws76">Estos de-</div><div class="t m0 x6 h5 y68 ff5 fs3 fc0 sc0 ls1 ws77">\ufb01nen un <span class="ff7 ws78">vidrio de<span class="_9 blank"> </span>espines </span><span class="ws79">como<span class="_9 blank"> </span>un sistema<span class="_9 blank"> </span>de <span class="ff8 ls64">N</span><span class="ws7a">espines<span class="_1a blank"> </span>lo calizados</span></span></div><div class="t m0 x6 h5 y69 ff5 fs3 fc0 sc0 ls1 ws7b">en los nudos de una red <span class="ff8 ws51">d</span><span class="ws7c">-dimensional \u039b<span class="ff8 ls65">,</span><span class="ws7d">interactuando median<span class="_17 blank"></span>te <span class="ff8 ls66">J</span><span class="ffc fs4 v5">xy</span></span></span></div><div class="t m0 x6 h5 y6a ff5 fs3 fc0 sc0 ls1 wse">(aleatorias)<span class="_8 blank"> </span>y<span class="_8 blank"> </span>ro deados<span class="_8 blank"> </span>de<span class="_8 blank"> </span>un<span class="_8 blank"> </span>ba\u02dc<span class="_5 blank"></span>no<span class="_8 blank"> </span>t<span class="_17 blank"></span>´<span class="_7 blank"></span>ermico<span class="_8 blank"> </span>a<span class="_8 blank"> </span>temp eratura<span class="_8 blank"> </span><span class="ff8 ls67">T</span>.</div><div class="t m0 x4 h4 y6b ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws7e">La aleatoriedad in<span class="_6 blank"></span>tro<span class="_4 blank"> </span>duce problemas te´<span class="_5 blank"></span>oricos en el marco de la Mec´<span class="_5 blank"></span>anica</span></div><div class="t m0 x6 h5 y6c ff5 fs3 fc0 sc0 ls1 ws7f">Estad<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131stica, incluso en el caso de equilibrio.<span class="_9 blank"> </span>No p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>demos considerar un</div><div class="t m0 x6 h5 y6d ff5 fs3 fc0 sc0 ls1 ws80">hamiltoniano concreto <span class="ff8 ls68">H<span class="ffc fs4 ls69 v5">J</span></span><span class="ws2a">(<span class="ffe ws50">s</span><span class="ws81">) con una con\ufb01guraci´<span class="_5 blank"></span>on<span class="_12 blank"> </span>concreta de <span class="ffe ws50">J</span><span class="ws82">\u2019s y</span></span></span></div><div class="t m0 x6 h5 y6e ff5 fs3 fc0 sc0 ls1 ws43">de <span class="ffe ws50">s</span><span class="ws83">\u2019s, puesto que no existe con\ufb01guraci´<span class="_5 blank"></span>on ´<span class="_5 blank"></span>unica que minimice la<span class="_15 blank"> </span>energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a</span></div><div class="t m0 x6 h5 y5 ff5 fs3 fc0 sc0 ls6a">a<span class="ff8 ls6b">T</span><span class="ls1 ws84">= 0<span class="ff8 ls6c">.</span><span class="ws85">Deb emos<span class="_8 blank"> </span>considerar<span class="_8 blank"> </span>un<span class="_8 blank"> </span>conjunto<span class="_8 blank"> </span>de<span class="_8 blank"> </span>hamiltonianos,<span class="_8 blank"> </span>cada<span class="_8 blank"> </span>uno</span></span></div><div class="t m0 x6 h5 y6f ff5 fs3 fc0 sc0 ls1 ws86">de los cuales constituye una muestra particular o <span class="ff7 ws87">r´<span class="_5 blank"></span>eplic<span class="_17 blank"></span>a <span class="ff5 ws88">de nuestro</span></span></div><div class="t m0 x6 h5 y70 ff5 fs3 fc0 sc0 ls1 ws89">sistema f<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131sico.</div><div class="t m0 x4 h4 y71 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws8a">En sistemas macrosc´<span class="_5 blank"></span>opicos (<span class="ff8 ls6d">N</span><span class="ff4 ws8b">\u2192 \u221e</span><span class="ws8c">),<span class="_10 blank"> </span>el promedio estad<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131stico nos</span></span></div><div class="t m0 x6 h5 y72 ff5 fs3 fc0 sc0 ls1 ws8d">a<span class="_6 blank"></span>yuda a solucionar este<span class="_13 blank"> </span>problema pues las<span class="_13 blank"> </span>\ufb02uctuaciones<span class="_1a blank"> </span>relativ<span class="_6 blank"></span>as de</div><div class="t m0 x6 h1f y73 ff5 fs3 fc0 sc0 ls1 ws59">la energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a en<span class="_6 blank"></span>torno a su v<span class="_17 blank"></span>alor medio son <span class="ff8 ls6e">O</span><span class="ws2a">(<span class="ff8 ls6f">N</span><span class="ffd fs4 ws52 v3">\u2212<span class="ff9 ws53">1<span class="ffa ws14">/</span><span class="ls70">2</span></span></span><span class="ws8e">).<span class="_1c blank"> </span>Ser<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a con<span class="_6 blank"></span>v<span class="_6 blank"></span>enien<span class="_6 blank"></span>te</span></span></div><div class="t m0 x6 h5 y74 ff5 fs3 fc0 sc0 ls1 ws33">que<span class="_9 blank"> </span>las<span class="_9 blank"> </span>\ufb02uctuaciones<span class="_9 blank"> </span>en<span class="_9 blank"> </span>la<span class="_9 blank"> </span>energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a,<span class="_9 blank"> </span>debidas<span class="_9 blank"> </span>a<span class="_9 blank"> </span>la<span class="_9 blank"> </span>p osibilidad<span class="_9 blank"> </span>de<span class="_9 blank"> </span>tener</div><div class="t m0 x6 h4 y75 ff5 fs3 fc0 sc0 ls1 ws5a">diferen<span class="_6 blank"></span>tes r´<span class="_5 blank"></span>eplicas,<span class="_9 blank"> </span>tam<span class="_6 blank"></span>bi<span class="_6 blank"></span>´<span class="_7 blank"></span>en fuesen n<span class="_6 blank"></span>ulas en <span class="ff8 ls71">N</span><span class="ff4 ws8f">\u2192 \u221e</span><span class="ws37">.<span class="_1c blank"> </span>Cuando<span class="_a blank"> </span>o curre</span></div><div class="t m0 x6 h5 y76 ff5 fs3 fc0 sc0 ls1 ws90">esto se<span class="_11 blank"> </span>dice<span class="_11 blank"> </span>que<span class="_14 blank"> </span>la energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a del sistema<span class="_14 blank"> </span>(u otra magnitud extensiv<span class="_17 blank"></span>a</div><div class="t m0 x6 h5 y77 ff5 fs3 fc0 sc0 ls1 ws91">que<span class="_8 blank"> </span>\ufb02uct ´<span class="_5 blank"></span>ua)<span class="ff7 ws92">auto-pr<span class="_17 blank"></span>ome<span class="_17 blank"></span>dia <span class="ff5 ws93">(p ermiten<span class="_8 blank"> </span>deriv<span class="_17 blank"></span>aciones<span class="_8 blank"> </span>te´<span class="_5 blank"></span>oricas<span class="_8 blank"> </span>de<span class="_8 blank"> </span>ese<span class="_8 blank"> </span>v<span class="_17 blank"></span>alor</span></span></div><div class="t m0 x6 h5 y78 ff5 fs3 fc0 sc0 ls1">medio)</div><div class="t m0 x4 h4 y79 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws33">En<span class="_16 blank"> </span>Mec´<span class="_5 blank"></span>anica<span class="_16 blank"> </span>Estad<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131stica<span class="_16 blank"> </span>de<span class="_16 blank"> </span>sistemas<span class="_16 blank"> </span>aleatorios<span class="_16 blank"> </span>p o demos<span class="_16 blank"> </span>distinguir<span class="_16 blank"> </span>dos</span></div><div class="t m0 x6 h5 y7a ff5 fs3 fc0 sc0 ls1 ws94">tip os<span class="_8 blank"> </span>de<span class="_8 blank"> </span>promedios:</div><div class="t m0 x0 h5 y7b ffe fs3 fc0 sc0 ls72">\u2013<span class="ff5 ls1 ws95">Promedio t<span class="_6 blank"></span>´<span class="_7 blank"></span>ermico, que<span class="_16 blank"> </span>se realiza<span class="_16 blank"> </span>sobre cada nuestra macrosc´<span class="_5 blank"></span>opica</span></div><div class="t m0 x21 h5 y7c ff5 fs3 fc0 sc0 ls1 ws96">del sistema.</div><div class="t m0 x0 h5 y7d ffe fs3 fc0 sc0 ls72">\u2013<span class="ff5 ls1 ws97">Promedio sobre la distribuci´<span class="_5 blank"></span>on de<span class="_1a blank"> </span>par´<span class="_5 blank"></span>ametros aleatorios (desor-</span></div><div class="t m0 x21 h5 y7e ff5 fs3 fc0 sc0 ls1 ws98">den) que caracteriza cada sistema.<span class="_1d blank"> </span>En el caso de los <span class="ff7 ws99">vidrios de</span></div><div class="t m0 x21 h5 y7f ff7 fs3 fc0 sc0 ls1 ws9a">espines <span class="ff5 ws9b">estos par´<span class="_5 blank"></span>ametros son<span class="_13 blank"> </span>las interacciones <span class="ff8 ls73">J</span><span class="ffc fs4 ws2b v5">xy </span><span class="ff8 ls74">.</span><span class="ws9c">Este ´<span class="_5 blank"></span>ultimo</span></span></div><div class="t m0 x21 h4 y80 ff5 fs3 fc0 sc0 ls1 ws33">promedio<span class="_16 blank"> </span>lo<span class="_16 blank"> </span>denotamos<span class="_8 blank"> </span>p or<span class="_16 blank"> </span><span class="ff4 ws9d">hh·ii </span><span class="ws9e">que<span class="_8 blank"> </span>puede<span class="_16 blank"> </span>llev<span class="_6 blank"></span>arse<span class="_16 blank"> </span>a<span class="_16 blank"> </span>cab o<span class="_8 blank"> </span>de<span class="_16 blank"> </span>dos</span></div><div class="t m0 x21 h5 y81 ff5 fs3 fc0 sc0 ls1 ws9f">formas diferen<span class="_6 blank"></span>tes, dep<span class="_4 blank"> </span>endiendo<span class="_a blank"> </span>de la naturaleza<span class="_a blank"> </span>de la interacci´<span class="_5 blank"></span>on</div><div class="t m0 x21 h5 y82 ff5 fs3 fc0 sc0 ls1 ws4">de in<span class="_6 blank"></span>tercam<span class="_6 blank"></span>bio <span class="ff8 ls75">J</span><span class="ffc fs4 ws2b v5">xy </span>.</div><div class="t m0 x4 h4 y2e ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 ws83">Las can<span class="_6 blank"></span>tidades f<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131sicas que queremos<span class="_16 blank"> </span>promediar se<span class="_16 blank"> </span>expresan<span class="_16 blank"> </span>en t´<span class="_5 blank"></span>erminos</span></div><div class="t m0 x6 h5 y2f ff5 fs3 fc0 sc0 ls1 ws5a">de deriv<span class="_17 blank"></span>adas de la energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a libre con respecto<span class="_9 blank"> </span>a campos auxiliares.<span class="_18 blank"> </span>El</div><div class="t m0 x5 h5 y30 ff5 fs3 fc0 sc0 ls1">7</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><div class="t m0 x6 h5 yb ff5 fs3 fc0 sc0 ls1 wsa0">c´<span class="_5 blank"></span>alculo de la energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a libre inv<span class="_17 blank"></span>olucra promediar sobre la distribuci´<span class="_5 blank"></span>on</div><div class="t m0 x6 h5 y40 ff5 fs3 fc0 sc0 ls1 wsa1">de los par´<span class="_5 blank"></span>ametros aleatorios.<span class="_18 blank"> </span>Este promedio sobre el desorden puede</div><div class="t m0 x6 h5 y41 ff5 fs3 fc0 sc0 ls1 ws4">llev<span class="_17 blank"></span>arse a cab<span class="_4 blank"> </span>o de dos formas diferen<span class="_6 blank"></span>tes, dep<span class="_4 blank"> </span>endiendo<span class="_a blank"> </span>de la naturaleza</div><div class="t m0 x6 h5 y42 ff5 fs3 fc0 sc0 ls1 ws4">de la in<span class="_6 blank"></span>teracci´<span class="_5 blank"></span>on de intercam<span class="_17 blank"></span>bio <span class="ff8 ls76">J</span><span class="ffc fs4 ws2b v5">xy </span>:</div><div class="t m0 x0 h5 y83 ffe fs3 fc0 sc0 ls72">\u2013<span class="ff5 ls1 wsa2">Si las <span class="ff8 ls77">J</span><span class="ffc fs4 wsa3 v5">xy </span><span class="wsa4">v<span class="_17 blank"></span>ar<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131an<span class="_8 blank"> </span>muy<span class="_8 blank"> </span>r´<span class="_5 blank"></span>apidamente,<span class="_a blank"> </span>comparado<span class="_a blank"> </span>con<span class="_a blank"> </span>el<span class="_a blank"> </span>tiemp o<span class="_12 blank"> </span>de</span></span></div><div class="t m0 x21 h5 y84 ff5 fs3 fc0 sc0 ls1 wsa5">observ<span class="_17 blank"></span>aci´<span class="_5 blank"></span>on,<span class="_15 blank"> </span>pueden<span class="_1e blank"> </span>ser<span class="_1e blank"> </span>consideradas<span class="_1e blank"> </span>como<span class="_1e blank"> </span>v<span class="_17 blank"></span>ariables<span class="_1e blank"> </span>termodin´<span class="_5 blank"></span>amicas,</div><div class="t m0 x21 h5 y85 ff5 fs3 fc0 sc0 ls1 wsa6">tratadas de igual<span class="_12 blank"> </span>forma que los<span class="_12 blank"> </span>espines,<span class="_12 blank"> </span>de<span class="_12 blank"> </span>forma que la<span class="_12 blank"> </span>funci´<span class="_5 blank"></span>on</div><div class="t m0 x21 h5 y86 ff5 fs3 fc0 sc0 ls1 wsa7">de partici´<span class="_5 blank"></span>on ser<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a:</div><div class="t m0 x22 h20 y87 ff8 fs3 fc0 sc0 ls78">Z<span class="ffa fs4 ls79 v5">a</span><span class="ff5 ls2c">=<span class="ff4 ls1 ws17">hh</span></span><span class="ls7a">Z<span class="ffc fs4 ls7b v5">J</span><span class="ff4 ls1 wsa8">ii \u2261 <span class="ffb fs5 ls7c v15">Z</span></span><span class="ls1 ws51">d<span class="ffe ls7d">J</span><span class="ffb fs5 ve">X</span></span></span></div><div class="t m0 x23 hd y88 ffc fs4 fc0 sc0 ls1">s</div><div class="t m0 x24 h21 y89 ff8 fs3 fc0 sc0 ls7e">P<span class="ff5 ls1 ws2a">(<span class="ffe ws50">J</span>)</span><span class="ls7f">e<span class="ff4 ls1 ws17 v6">\u2212</span><span class="ls1 wsa9 v6">\u03b2 H</span><span class="ffc fs4 ls7b v14">J</span><span class="ff5 ls1 ws2a v6">(<span class="ffe ws50">s<span class="ff5 ls80">)<span class="ls1 v16">(7)</span></span></span></span></span></div><div class="t m0 x21 h5 y8a ff5 fs3 fc0 sc0 ls1 ws20">y la energ<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131a libre del sistema<span class="_a blank"> </span>ser<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a</div><div class="t m0 x25 h4 y8b ff8 fs3 fc0 sc0 ls81">F<span class="ffa fs4 ls82 v5">a</span><span class="ff5 ls83">=<span class="ff4 ls1 ws17">\u2212</span></span><span class="ls84">K<span class="ffa fs4 ls85 v5">B</span><span class="ls86">T<span class="ff5 ls1 wsaa">ln </span><span class="ls87">Z<span class="ffa fs4 ls88 v5">a</span><span class="ls89">.<span class="ff5 ls1">(8)</span></span></span></span></span></div><div class="t m0 x21 h5 y8c ff5 fs3 fc0 sc0 ls1 wsab">Las v<span class="_17 blank"></span>ariables<span class="_13 blank"> </span>interacciones est´<span class="_5 blank"></span>an en equilibrio<span class="_11 blank"> </span>con las v<span class="_17 blank"></span>ariables</div><div class="t m0 x21 h5 y8d ff5 fs3 fc0 sc0 ls1 wsac">espines,<span class="_12 blank"> </span>y<span class="_a blank"> </span>ambas<span class="_a blank"> </span>tienen<span class="_a blank"> </span>la<span class="_a blank"> </span>lib ertad<span class="_12 blank"> </span>de<span class="_a blank"> </span>tomar<span class="_a blank"> </span>cualquier<span class="_12 blank"> </span>v<span class="_17 blank"></span>alor<span class="_a blank"> </span>que</div><div class="t m0 x21 h5 y8e ff5 fs3 fc0 sc0 ls1 wsad">tienda a minimizar <span class="ff8 ls8a">H<span class="ffc fs4 ls8b v5">J</span></span><span class="ws2a">(<span class="ffe ws50">s</span><span class="ws21">).<span class="_1f blank"> </span>Este<span class="_1a blank"> </span>promedio<span class="_13 blank"> </span>recib e<span class="_13 blank"> </span>el<span class="_1a blank"> </span>nombre<span class="_1a blank"> </span>de</span></span></div><div class="t m0 x21 h5 y8f ff7 fs3 fc0 sc0 ls1 wsae">pr<span class="_17 blank"></span>ome<span class="_17 blank"></span>dio de r<span class="_6 blank"></span>e<span class="_17 blank"></span>c<span class="_17 blank"></span>o<span class="_6 blank"></span>cido<span class="ff5">.</span></div><div class="t m0 x0 h5 y90 ffe fs3 fc0 sc0 ls72">\u2013<span class="ff5 ls1 wsaf">Esto<span class="_a blank"> </span>no<span class="_a blank"> </span>o curre<span class="_a blank"> </span>en<span class="_a blank"> </span>los<span class="_a blank"> </span><span class="ff7 wsb0">vidrios de espines</span><span class="wsa2">, en los<span class="_12 blank"> </span>que las </span></span><span class="ls1 ws50">J<span class="ff5 wsb1">\u2019s est´<span class="_5 blank"></span>an</span></span></div><div class="t m0 x21 h5 y91 ff5 fs3 fc0 sc0 ls1 wsb2">\ufb01jas para cada m<span class="_6 blank"></span>uestra macrosc´<span class="_5 blank"></span>opica del<span class="_13 blank"> </span>sistema.<span class="_20 blank"> </span>Los espines</div><div class="t m0 x21 h5 y92 ff5 fs3 fc0 sc0 ls1 ws33">pueden<span class="_8 blank"> </span>v<span class="_6 blank"></span>ariar<span class="_8 blank"> </span>en<span class="_8 blank"> </span>respuesta<span class="_a blank"> </span>a<span class="_8 blank"> </span>esas<span class="_a blank"> </span>in<span class="_6 blank"></span>teracciones,<span class="_a blank"> </span>p ero<span class="_8 blank"> </span>no<span class="_8 blank"> </span>al<span class="_a blank"> </span>rev<span class="_6 blank"></span>´<span class="_7 blank"></span>es.</div><div class="t m0 x21 h5 y93 ff5 fs3 fc0 sc0 ls1 ws39">Se dice entonces que las <span class="ffe ws50">J</span><span class="wsb3">\u2019s son<span class="_9 blank"> </span>v<span class="_17 blank"></span>ariables<span class="_9 blank"> </span><span class="ff7 wsf">\ufb01jas</span><span class="wsb4">.<span class="_18 blank"> </span>En<span class="_9 blank"> </span>este caso se</span></span></div><div class="t m0 x21 h5 y94 ff5 fs3 fc0 sc0 ls1 wsb5">promedian cantidades macrosc´<span class="_5 blank"></span>opicas como la energ<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131a libre sobre</div><div class="t m0 x21 h5 y95 ff5 fs3 fc0 sc0 ls1 ws20">la distribuci´<span class="_5 blank"></span>on de<span class="_8 blank"> </span>par´<span class="_5 blank"></span>ametros<span class="_8 blank"> </span>aleatorios:</div><div class="t m0 x26 h4 y96 ff8 fs3 fc0 sc0 ls8c">F<span class="ffa fs4 ls8d v5">q</span><span class="ff5 ls83">=<span class="ff4 ls1 ws17">hh</span></span><span class="ls8e">F<span class="ffc fs4 ls7b v5">J</span><span class="ff4 ls1 wsa8">ii <span class="ff5 ls2c">=</span><span class="ws17">\u2212</span></span><span class="ls8f">K<span class="ffa fs4 ls90 v5">B</span><span class="ls91">T<span class="ff4 ls1 ws17">hh<span class="ff5 wsb6">ln </span></span><span class="ls92">Z<span class="ffc fs4 ls8b v5">J</span><span class="ff4 ls1 ws17">ii</span><span class="ls93">.<span class="ff5 ls1">(9)</span></span></span></span></span></span></div><div class="t m0 x21 h5 y97 ff5 fs3 fc0 sc0 ls1 wsb7">Sin embargo, desde un punto de vista matem´<span class="_5 blank"></span>atico,<span class="_12 blank"> </span>el promediar</div><div class="t m0 x21 h5 y98 ff5 fs3 fc0 sc0 ls1 ws9f">la energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a libre<span class="_a blank"> </span>es muc<span class="_17 blank"></span>ho<span class="_a blank"> </span>m´<span class="_5 blank"></span>as<span class="_a blank"> </span>dif<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131cil que promediar la funci´<span class="_5 blank"></span>on<span class="_a blank"> </span>de</div><div class="t m0 x21 h5 y99 ff5 fs3 fc0 sc0 ls1 wsb8">partici´<span class="_5 blank"></span>on.<span class="_9 blank"> </span>P<span class="_6 blank"></span>ara<span class="_15 blank"> </span>solucionar<span class="_16 blank"> </span>esto<span class="_15 blank"> </span>se<span class="_16 blank"> </span>utiliza<span class="_15 blank"> </span>la<span class="_16 blank"> </span>t<span class="_6 blank"></span>´<span class="_7 blank"></span>ecnica<span class="_15 blank"> </span>de<span class="_16 blank"> </span>r´<span class="_5 blank"></span>eplicas.[10]</div><div class="t m0 x4 h4 y9a ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 wsb9">Otro problema que tenemos<span class="_1a blank"> </span>en los<span class="_9 blank"> </span><span class="ff7 wsba">vidrios<span class="_9 blank"> </span>de<span class="_9 blank"> </span>espines </span><span class="wsbb">es el problema</span></span></div><div class="t m0 x6 h5 y9b ff5 fs3 fc0 sc0 ls1 wsbc">de la <span class="ff7 wsf">er<span class="_17 blank"></span>go<span class="_17 blank"></span>dicidad<span class="ff5 wsbd">.<span class="_9 blank"> </span>Los </span><span class="wsbe">vidrios<span class="_8 blank"> </span>de<span class="_8 blank"> </span>espines <span class="ff5 wsbf">son<span class="_16 blank"> </span>sistemas<span class="_8 blank"> </span>no<span class="_8 blank"> </span>erg´<span class="_5 blank"></span>odicos<span class="_16 blank"> </span>p or</span></span></span></div><div class="t m0 x6 h5 y9c ff5 fs3 fc0 sc0 ls1 wsc0">la existencia de un gran n´<span class="_5 blank"></span>umero de estados fundamen<span class="_17 blank"></span>tales degenera-</div><div class="t m0 x6 h5 y9d ff5 fs3 fc0 sc0 ls1 wsc1">dos que<span class="_a blank"> </span>no est´<span class="_5 blank"></span>an relacionados<span class="_a blank"> </span>unos con otros a<span class="_a blank"> </span>tra<span class="_6 blank"></span>v<span class="_6 blank"></span>´<span class="_7 blank"></span>es de<span class="_a blank"> </span>una simetr<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a</div><div class="t m0 x6 h5 y9e ff5 fs3 fc0 sc0 ls1">sencilla.</div><div class="t m0 x5 h5 y9f ff5 fs3 fc0 sc0 ls1">8</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi xa ya0 w5 h22" alt="" src="https://files.passeidireto.com/114c34d8-79c3-4edb-9279-20b76f8c5573/bg9.png"><div class="t m0 x3 h7 yb ff6 fs1 fc0 sc0 ls1 wsc2">2.4<span class="_c blank"> </span>Mo delo<span class="_1a blank"> </span>de<span class="_1a blank"> </span>Edw<span class="_6 blank"></span>ards-Anderson</div><div class="t m0 x3 h5 y44 ff5 fs3 fc0 sc0 ls1 wsc3">Incluso<span class="_15 blank"> </span>con<span class="_1e blank"> </span>los<span class="_15 blank"> </span>m´<span class="_5 blank"></span>eto dos<span class="_1e blank"> </span>m´<span class="_5 blank"></span>as<span class="_15 blank"> </span>p otentes<span class="_1e blank"> </span>de<span class="_15 blank"> </span>la<span class="_1e blank"> </span>Mec´<span class="_5 blank"></span>anica<span class="_15 blank"> </span>Estad<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131stica,<span class="_15 blank"> </span>es<span class="_1e blank"> </span>dif<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131cil<span class="_1e blank"> </span>es-</div><div class="t m0 x3 h5 y45 ff5 fs3 fc0 sc0 ls1 ws8">tudiar<span class="_15 blank"> </span>mo delos<span class="_16 blank"> </span>realistas<span class="_16 blank"> </span>de<span class="_16 blank"> </span>materiales<span class="_16 blank"> </span>magn<span class="_6 blank"></span>´<span class="_7 blank"></span>eticos<span class="_15 blank"> </span>aleatorios,<span class="_16 blank"> </span>excepto<span class="_16 blank"> </span>cuando</div><div class="t m0 x3 h5 y46 ff5 fs3 fc0 sc0 ls1 wsc4">hacemos sim<span class="_6 blank"></span>ulaci´<span class="_5 blank"></span>on n<span class="_6 blank"></span>um<span class="_6 blank"></span>´<span class="_7 blank"></span>erica.</div><div class="t m0 x4 h5 y47 ff5 fs3 fc0 sc0 ls1 ws8">Edw<span class="_6 blank"></span>ards<span class="_1a blank"> </span>y<span class="_13 blank"> </span>Anderson<span class="_13 blank"> </span>[5]<span class="_1a blank"> </span>propusieron<span class="_13 blank"> </span>un<span class="_1a blank"> </span>mo delo<span class="_1a blank"> </span>simpli\ufb01cado<span class="_13 blank"> </span>de<span class="_13 blank"> </span><span class="ff7">vidrio</span></div><div class="t m0 x3 h5 ya1 ff7 fs3 fc0 sc0 ls1 wsc5">de<span class="_a blank"> </span>espines <span class="ff5 wsc6">de equilibrio,<span class="_12 blank"> </span>una de cuy<span class="_6 blank"></span>as versiones, al menos, puede<span class="_12 blank"> </span>resolv<span class="_6 blank"></span>erse</span></div><div class="t m0 x3 h5 ya2 ff5 fs3 fc0 sc0 ls1 ws2a">exactamen<span class="_6 blank"></span>te.</div><div class="t m0 x4 h4 y69 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 wsc7">Sea un conjunto de <span class="ff8 ls94">N</span><span class="wsc8">espines en un red<span class="_8 blank"> </span>\u039b, con energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a con\ufb01guracional</span></span></div><div class="t m0 x27 h23 ya3 ff8 fs3 fc0 sc0 ls95">H<span class="ff5 ls1 ws2a">(<span class="ffe ws50">J</span></span><span class="ls96">,<span class="ffe ls1 ws50">s<span class="ff5 ws1b">) = <span class="ff4 ls97">\u2212</span><span class="va">1</span></span></span></span></div><div class="t m0 x28 h24 ya4 ff5 fs3 fc0 sc0 ls98">2<span class="ffb fs5 ls1 v10">X</span></div><div class="t m0 x29 h8 ya5 ffc fs4 fc0 sc0 ls1 ws15">x<span class="ffa ws14">,</span>y</div><div class="t m0 x2a h25 ya3 ff8 fs3 fc0 sc0 ls59">J<span class="ffc fs4 ls1 ws2b v5">xy </span><span class="ls6">s<span class="ffc fs4 ls39 v5">x</span>s<span class="ffc fs4 ls3d v5">y</span><span class="ff4 ls3e">\u2212</span><span class="ls99">h<span class="ffb fs5 ls1 ve">X</span></span></span></div><div class="t m0 x2b hd ya6 ffc fs4 fc0 sc0 ls1">x</div><div class="t m0 x2c h5 ya7 ff8 fs3 fc0 sc0 ls6">s<span class="ffc fs4 ls9a v5">x</span><span class="ff5 ls1">(10)</span></div><div class="t m0 x6 h5 ya8 ff5 fs3 fc0 sc0 ls1 wsc9">donde las in<span class="_6 blank"></span>teracciones <span class="ff8 ls9b">J</span><span class="ffc fs4 wsca v5">xy </span><span class="wscb">son<span class="_16 blank"> </span>v<span class="_6 blank"></span>ariables<span class="_16 blank"> </span>aleatorias<span class="_16 blank"> </span>indep endientes<span class="_16 blank"> </span>dis-</span></div><div class="t m0 x6 h5 ya9 ff5 fs3 fc0 sc0 ls1 ws33">tribuidas<span class="_8 blank"> </span>espacialmen<span class="_17 blank"></span>te<span class="_a blank"> </span>p or<span class="_16 blank"> </span>la<span class="_8 blank"> </span>red,<span class="_8 blank"> </span>por<span class="_8 blank"> </span>ejemplo<span class="_8 blank"> </span>distribuci´<span class="_5 blank"></span>on<span class="_16 blank"> </span><span class="ff8 ls7e">P</span><span class="ws2a">(<span class="ffe ws50">J</span><span class="wscc">), que</span></span></div><div class="t m0 x6 h5 yaa ff5 fs3 fc0 sc0 ls1 wscd">puede ser gaussiana:</div><div class="t m0 x2d h25 yab ff8 fs3 fc0 sc0 ls7e">P<span class="ff5 ls1 ws2a">(<span class="ffe ws50">J</span><span class="wsce">) = <span class="ffb fs5 ve">Y</span></span></span></div><div class="t m0 x2e h8 yac ffc fs4 fc0 sc0 ls1 ws15">x<span class="ffa ws14">,</span>y</div><div class="t m0 x2f h26 yad ffb fs5 fc0 sc0 ls1">\uf8f1</div><div class="t m0 x2f h26 yae ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x2f h26 yaf ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x2f h26 yb0 ffb fs5 fc0 sc0 ls1">\uf8f2</div><div class="t m0 x2f h26 yb1 ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x2f h26 yb2 ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x2f h26 yb3 ffb fs5 fc0 sc0 ls1">\uf8f3</div><div class="t m0 x19 h5 yb4 ff5 fs3 fc0 sc0 ls1">1</div><div class="t m0 xa h26 yb5 ffb fs5 fc0 sc0 ls9c">q<span class="ff5 fs3 ls1 ws2a v17">2<span class="ff8 wscf">\u03c0 \u03c3 <span class="ff9 fs4 v3">2</span></span></span></div><div class="t m0 x17 hd yb6 ffc fs4 fc0 sc0 ls1">J</div><div class="t m0 x30 h5 yb7 ff8 fs3 fc0 sc0 ls1">e</div><div class="t m0 x1e h27 yb8 ffd fs4 fc0 sc0 ls9d">\u2212<span class="ff5 fs3 ls1 ws2a v18">(<span class="ff8 ls9e">J</span></span><span class="ffc ls1 wsd0 v3">xy </span><span class="ff4 fs3 ls9f v18">\u2212<span class="ff5 ls1 v14">¯</span></span></div><div class="t m0 x31 h28 yb9 ff8 fs3 fc0 sc0 ls59">J<span class="ffc fs4 ls1 ws2b v5">xy </span><span class="ff5 lsa0">)<span class="ff9 fs4 ls1 v3">2</span></span></div><div class="t m0 x32 h29 yba ff5 fs3 fc0 sc0 ls1 ws2a">2<span class="ff8 lsa1">\u03c3</span><span class="ff9 fs4 v3">2</span></div><div class="t m0 x33 h2a ybb ffc fs4 fc0 sc0 lsa2">J<span class="ffb fs5 ls1 v19">\uf8fc</span></div><div class="t m0 x34 h26 ybc ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x34 h26 ybd ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x34 h26 ybe ffb fs5 fc0 sc0 ls1">\uf8fd</div><div class="t m0 x34 h26 ybf ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x34 h26 yc0 ffb fs5 fc0 sc0 ls1">\uf8f4</div><div class="t m0 x34 h26 yc1 ffb fs5 fc0 sc0 ls1">\uf8fe</div><div class="t m0 x35 h5 yc2 ff5 fs3 fc0 sc0 ls1">(11)</div><div class="t m0 x6 h1e yc3 ff5 fs3 fc0 sc0 ls1 wsd1">Si <span class="v14">¯</span></div><div class="t m0 x0 h4 yc3 ff8 fs3 fc0 sc0 ls59">J<span class="ffc fs4 ls1 ws2d v5">xy </span><span class="ff5 ls83">=</span><span class="lsa3">J<span class="ff9 fs4 lsa4 v5">0</span><span class="lsa5">,<span class="ff4 ls1 ws17">\u2200<span class="ff5 ws2a">(<span class="ffe ws50">x</span></span></span><span class="ls96">,<span class="ffe ls20">y<span class="ff5 ls1 wscb">),<span class="_16 blank"> </span>indep endiente<span class="_16 blank"> </span>de<span class="_16 blank"> </span>la<span class="_16 blank"> </span>distancia<span class="_8 blank"> </span>en<span class="_17 blank"></span>tre<span class="_8 blank"> </span>espines,<span class="_16 blank"> </span>tene-</span></span></span></span></span></div><div class="t m0 x6 h5 yc4 ff5 fs3 fc0 sc0 ls1 ws8">mos<span class="_16 blank"> </span>el<span class="_16 blank"> </span>mo delo<span class="_16 blank"> </span>SK,<span class="_16 blank"> </span>[10]<span class="_15 blank"> </span>o<span class="_16 blank"> </span>mo delo<span class="_16 blank"> </span>de<span class="_16 blank"> </span><span class="ff7 wsd2">vidrio<span class="_8 blank"> </span>de<span class="_16 blank"> </span>espines </span><span class="wsd3">de<span class="_16 blank"> </span>rango in\ufb01nito,</span></div><div class="t m0 x6 h5 yc5 ff5 fs3 fc0 sc0 ls1 ws84">que puede resolverse.<span class="_9 blank"> </span>Se calcula la energ<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a libre del sistema en la forma</div><div class="t m0 x36 h4 yc6 ff8 fs3 fc0 sc0 lsa6">F<span class="ff5 ls83">=<span class="ff4 ls1 ws17">\u2212</span></span><span class="lsa7">k<span class="ffa fs4 ls85 v5">B</span><span class="ls91">T<span class="ff4 ls1 ws17">hh<span class="ff5 wsb6">ln </span></span><span class="lsa8">Z<span class="ff4 ls1 wsd4">ii <span class="ff5">(12)</span></span></span></span></span></div><div class="t m0 x6 h5 yc7 ff5 fs3 fc0 sc0 ls1 wsd5">utilizando la t<span class="_6 blank"></span>´<span class="_7 blank"></span>ecnica de r´<span class="_5 blank"></span>eplicas.<span class="_1a blank"> </span>Consite en hacer la aproximaci´<span class="_5 blank"></span>on</div><div class="t m0 x36 h5 yc8 ff5 fs3 fc0 sc0 ls1 wsaa">ln <span class="ff8 lsa9">Z</span><span class="ws9f">= lim</span></div><div class="t m0 x16 h8 yc9 ffa fs4 fc0 sc0 ls1 ws14">n<span class="ffd ws52">\u2192<span class="ff9">0</span></span></div><div class="t m0 xc h1f yca ff8 fs3 fc0 sc0 lsaa">Z<span class="ffa fs4 lsab v3">n</span><span class="ff4 ls3e">\u2212<span class="ff5 ls1">1</span></span></div><div class="t m0 x37 h5 ycb ff8 fs3 fc0 sc0 ls1">n</div><div class="t m0 x6 h1f ycc ff5 fs3 fc0 sc0 ls1 wsd6">y promediar sobre<span class="_11 blank"> </span>el desorden<span class="_11 blank"> </span><span class="ff8 lsac">Z<span class="ffa fs4 lsad v3">n</span></span><span class="wsd7">(Ejercicio).<span class="_21 blank"> </span>P<span class="_6 blank"></span>ara <span class="ff8 lsae">T<span class="ff4 lsaf">\u2192</span></span><span class="wsd8">0,<span class="_11 blank"> </span>en el</span></span></div><div class="t m0 x6 h5 ycd ff5 fs3 fc0 sc0 ls1 ws70">con<span class="_6 blank"></span>texto de simetr<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131a de r<span class="_17 blank"></span>´<span class="_7 blank"></span>eplicas,<span class="_a blank"> </span>se encuen<span class="_6 blank"></span>tra un cambio de fase desde</div><div class="t m0 x6 h5 yce ff5 fs3 fc0 sc0 ls1 wsd9">una fase <span class="ff7 wsda">ferr<span class="_17 blank"></span>omagn´<span class="_5 blank"></span>etic<span class="_17 blank"></span>a <span class="ff5 wsdb">a una<span class="_12 blank"> </span>fase<span class="_9 blank"> </span></span><span class="wsdc">vidriosa <span class="ff5 wsdd">.<span class="_1c blank"> </span>El<span class="_9 blank"> </span>par´<span class="_5 blank"></span>ametro de orden</span></span></span></div><div class="t m0 x6 h5 ycf ff5 fs3 fc0 sc0 ls1 ws20">que caracteriza<span class="_8 blank"> </span>la fase<span class="_8 blank"> </span><span class="ff7 wsde">vidriosa </span>es</div><div class="t m0 x1d h2b y3c ff8 fs3 fc0 sc0 lsb0">q<span class="ff5 ls83">=<span class="ff4 ls1 ws17">hh</span></span><span class="lsb1">s<span class="ffc fs4 lsb2 v5">x</span><span class="ff4 ls40">i<span class="ff9 fs4 ls32 vf">2</span><span class="ls1 ws17">i</span></span><span class="lsb3">,<span class="ff5 ls1">(13)</span></span></span></div><div class="t m0 x6 h5 yd0 ff5 fs3 fc0 sc0 ls1 wsdf">y el orden ferromagn<span class="_6 blank"></span>´<span class="_7 blank"></span>etico viene dado p<span class="_4 blank"> </span>or el par´<span class="_5 blank"></span>ametro</div><div class="t m0 x1d h4 yd1 ff8 fs3 fc0 sc0 lsb4">m<span class="ff5 ls83">=<span class="ff4 ls1 ws17">hh</span></span><span class="lsb5">s<span class="ffc fs4 lsb6 v5">x</span><span class="ff4 ls1 ws17">ii</span><span class="lsb7">.<span class="ff5 ls1">(14)</span></span></span></div><div class="t m0 x5 h5 y30 ff5 fs3 fc0 sc0 ls1">9</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x38 yd2 w6 h2c" alt="" src="https://files.passeidireto.com/114c34d8-79c3-4edb-9279-20b76f8c5573/bga.png"><div class="t m0 x4 h4 yb ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 wsa5">En<span class="_8 blank"> </span>el<span class="_8 blank"> </span>l<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131mite<span class="_8 blank"> </span>termo din´<span class="_5 blank"></span>amico<span class="_8 blank"> </span>(<span class="ff8 lsb8">N</span><span class="ff4 ws62">\u2192 \u221e</span><span class="wse0">),<span class="_16 blank"> </span>usando<span class="_8 blank"> </span>el<span class="_8 blank"> </span>m´<span class="_5 blank"></span>eto do<span class="_8 blank"> </span>del<span class="_8 blank"> </span>pun<span class="_6 blank"></span>to<span class="_8 blank"> </span>de</span></span></div><div class="t m0 x6 h5 y40 ff5 fs3 fc0 sc0 ls1 wsd5">silla se puede ev<span class="_17 blank"></span>aluar la energ<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131a libre por esp<span class="_3 blank"></span>´<span class="_e blank"></span>\u0131n obteniendo</div><div class="t m0 x39 h2d yd3 ff8 fs3 fc0 sc0 lsb9">f<span class="ff5 ls83">=</span><span class="ls1 wse1">k T<span class="_16 blank"> </span><span class="ffb fs5 lsba v1a">\ue010</span><span class="ff5 lsbb">(</span><span class="ff7 v14">\u02dc</span></span></div><div class="t m0 x3a h2e yd3 ff7 fs3 fc0 sc0 lsbc">J<span class="ff9 fs4 ls32 v5">0</span><span class="ff8 ls12">m<span class="ff9 fs4 ls37 v6">2</span><span class="ls1 ws51">/<span class="ff5 ws2a">2</span><span class="wse1">k T<span class="_22 blank"> </span><span class="ff5 lsbd">)<span class="ff4 ls4a">\u2212</span><span class="lsbe">[</span></span><span class="ff7 v14">\u02dc</span></span></span></span></div><div class="t m0 x1e h2f yd3 ff7 fs3 fc0 sc0 lsbf">J<span class="ff9 fs4 ls32 v6">2</span><span class="ff5 ls1 wse2">(1 <span class="ff4 ls4a">\u2212<span class="ff8 ls58">q</span></span><span class="lsc0">)<span class="ff9 fs4 lsa4 v6">2</span></span><span class="ff8 ws51">/</span><span class="ws2a">4(<span class="ff8 wse1">k T<span class="_22 blank"> </span></span><span class="lsc1">)<span class="ff9 fs4 lsc2 v6">2</span></span>]</span></span></div><div class="t m0 x11 h30 yd4 ff4 fs3 fc0 sc0 ls1 ws17">\u2212<span class="ff5 ws2a">(2<span class="ff8 lsc3">\u03c0</span><span class="lsc4">)</span><span class="ffd fs4 ws52 v6">\u2212<span class="ff9 ws53">1<span class="ffa ws14">/</span><span class="lsc5">2<span class="ffb fs5 ls7c v1b">Z</span></span></span></span><span class="ff8 wse3 v0">dz <span class="ff5 wse4">exp(<span class="ff4 lsc6">\u2212</span><span class="va">1</span></span></span></span></div><div class="t m0 x1e h31 yd5 ff5 fs3 fc0 sc0 lsc7">2<span class="ff8 lsc8 va">z</span><span class="ff9 fs4 ls37 v1c">2</span><span class="ls1 wse5 va">) ln(2 cosh \u039e)<span class="_4 blank"> </span></span><span class="ffb fs5 lsc9 v1d">\ue013</span><span class="ls1 v1e">(15)</span></div><div class="t m0 x6 h2e yd6 ff5 fs3 fc0 sc0 ls1 wse6">con<span class="_8 blank"> </span>\u039e =<span class="_8 blank"> </span><span class="ff7 v14">\u02dc</span></div><div class="t m0 x3b h2e yd6 ff7 fs3 fc0 sc0 lsca">J<span class="ff9 fs4 ls37 v5">0</span><span class="ff8 lscb">m<span class="ff5 lscc">+</span></span><span class="ls1 v14">\u02dc</span></div><div class="t m0 x11 h29 yd6 ff7 fs3 fc0 sc0 lscd">J<span class="ff8 lsce">q<span class="ff9 fs4 ls1 ws53 v3">1<span class="ffa ws14">/<span class="ff9 lscf">2</span></span></span><span class="lsd0">z<span class="ff5 ls5d">+</span><span class="ls1 wse7">h, <span class="ff5">y</span></span></span></span></div><div class="t m0 x2d h15 yd7 ff8 fs3 fc0 sc0 lsb4">m<span class="ff5 lsd1">=<span class="ffb fs5 lsd2 v15">Z</span></span><span class="ls1 wse8">dz <span class="ff5 ws2a">(2</span><span class="lsc3">\u03c0<span class="ff5 lsd3">)</span></span><span class="ffd fs4 ws52 v6">\u2212<span class="ff9 ws53">1<span class="ffa ws14">/</span><span class="lsd4">2</span></span></span><span class="ff5 wse4">exp(<span class="ff4 lsd5">\u2212</span><span class="va">1</span></span></span></div><div class="t m0 x3c h32 yd8 ff5 fs3 fc0 sc0 lsd6">2<span class="ff8 lsd7 va">z</span><span class="ff9 fs4 lsd8 v1c">2</span><span class="ls1 wse9 va">) tanh \u039e<span class="ff8">,</span></span></div><div class="t m0 x2d h15 yd9 ff8 fs3 fc0 sc0 lsb0">q<span class="ff5 lsd9">=<span class="ffb fs5 ls7c v15">Z</span></span><span class="ls1 wse8">dz <span class="ff5 ws2a">(2</span><span class="lsc3">\u03c0<span class="ff5 lsda">)</span></span><span class="ffd fs4 ws52 v6">\u2212<span class="ff9 ws53">1<span class="ffa ws14">/</span><span class="lsdb">2</span></span></span><span class="ff5 wse4">exp(<span class="ff4 lsd5">\u2212</span><span class="va">1</span></span></span></div><div class="t m0 x3d h33 yda ff5 fs3 fc0 sc0 lsdc">2<span class="ff8 lsd7 va">z</span><span class="ff9 fs4 ls37 v1c">2</span><span class="ls1 wsea va">) tanh</span><span class="ff9 fs4 lsdd v1c">2</span><span class="ls1 ws2a va">\u039e<span class="ff8">.</span></span></div><div class="t m0 x35 h5 ydb ff5 fs3 fc0 sc0 ls1">(16)</div><div class="t m0 x3 h5 ydc ff5 fs3 fc0 sc0 ls1 wseb">Figure<span class="_16 blank"> </span>3:<span class="_9 blank"> </span>Comp ortamien<span class="_6 blank"></span>to<span class="_16 blank"> </span>del<span class="_16 blank"> </span>par´<span class="_5 blank"></span>ametro<span class="_16 blank"> </span>de<span class="_16 blank"> </span>orden<span class="_16 blank"> </span>ferromagn´<span class="_5 blank"></span>etico<span class="_16 blank"> </span>(m)<span class="_16 blank"> </span>y<span class="_8 blank"> </span>del</div><div class="t m0 x3 h5 ydd ff5 fs3 fc0 sc0 ls1 ws28">par´<span class="_5 blank"></span>ametro de orden <span class="ff8 lsde">q</span><span class="ws70">en fuci´<span class="_5 blank"></span>on de la temp<span class="_4 blank"> </span>eratura para diferen<span class="_17 blank"></span>tes<span class="_8 blank"> </span>v<span class="_6 blank"></span>alores de</span></div><div class="t m0 x3 h34 yde ff7 fs3 fc0 sc0 ls1">\u02dc</div><div class="t m0 x3 h2e ydf ff7 fs3 fc0 sc0 lsbc">J<span class="ff9 fs4 lsdf v5">0</span><span class="ff4 ls19">\u2261<span class="ff8 ls1 wsec">N J <span class="ff9 fs4 lse0 v5">0</span><span class="ff5 lse1">y</span><span class="ff7 v14">\u02dc</span></span></span></div><div class="t m0 x3e h1f ydf ff7 fs3 fc0 sc0 ls1 wsf">J<span class="ff5 ls83">=<span class="ff8 lse2">N</span></span><span class="ff9 fs4 ws53 v3">1<span class="ffa ws14">/<span class="ff9 lse3">2</span></span></span><span class="ff8 lse4">\u03c3<span class="ffa fs4 lse5 v5">J</span><span class="ls1">.</span></span></div><div class="t m0 x4 h4 ye0 ff4 fs3 fc0 sc0 ls0">\u2022<span class="ff5 ls1 wsed">El mo<span class="_4 blank"> </span>delo de EA y su version de rango in\ufb01nito (mo<span class="_4 blank"> </span>delo SK) tiene una</span></div><div class="t m0 x6 h5 ye1 ff5 fs3 fc0 sc0 ls1 ws4">serie de limitaciones:</div><div class="t m0 x3f h5 ye2 ff5 fs3 fc0 sc0 ls1 wsee">1.<span class="_13 blank"> </span>El desorden<span class="_8 blank"> </span>est´<span class="_5 blank"></span>a congelado (no hay posibilidad<span class="_8 blank"> </span>de difusi´<span class="_5 blank"></span>on de im-</div><div class="t m0 x21 h5 ye3 ff5 fs3 fc0 sc0 ls1 wsef">purezas magn´<span class="_5 blank"></span>eticas en el metal)</div><div class="t m0 x3f h5 y2e ff5 fs3 fc0 sc0 ls1 ws8">2.<span class="_13 blank"> </span>La<span class="_8 blank"> </span>soluci´<span class="_5 blank"></span>on<span class="_8 blank"> </span>del<span class="_8 blank"> </span>mo delo<span class="_8 blank"> </span>SK<span class="_8 blank"> </span>con<span class="_8 blank"> </span>simetr<span class="_0 blank"></span>´<span class="_e blank"></span>\u0131a<span class="_8 blank"> </span>de<span class="_8 blank"> </span>r<span class="_6 blank"></span>´<span class="_7 blank"></span>eplicas<span class="_8 blank"> </span>es<span class="_8 blank"> </span>inestable<span class="_8 blank"> </span>a</div><div class="t m0 x21 h5 y2f ff5 fs3 fc0 sc0 ls1 wse">ba jas<span class="_8 blank"> </span>temp eraturas<span class="_8 blank"> </span>(Almeida<span class="_a blank"> </span>and<span class="_8 blank"> </span>Thouless<span class="_8 blank"> </span>1978).</div><div class="t m0 x40 h5 y30 ff5 fs3 fc0 sc0 ls1">10</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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