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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Random Energy Model</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Das <b>Random Energy Model</b> (abgekürzt <i>REM</i>) ist ein Spielzeugmodell in der <a href="Statistische_Physik" title="Statistische Physik">statistischen Physik</a> der ungeordneten Systeme, das 1980<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> von <a href="Bernard_Derrida" title="Bernard Derrida">Bernard Derrida</a> vorgeschlagen wurde.
</p><p>Es beschreibt ein <a href="Physikalisches_System" title="Physikalisches System">System</a> mit folgenden drei Eigenschaften:
</p>
<ul><li>Es gibt <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{N}}">
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<annotation encoding="application/x-tex">{\displaystyle 2^{N}}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f3cc22b5fa0e34487c8a6153965408e004c6e253.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.854ex; height:2.676ex;" alt="{\displaystyle 2^{N}}" loading="lazy"></span> <a href="Zustand_(Thermodynamik)" title="Zustand (Thermodynamik)">Zustände</a> mit Energien <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{i}}">
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<annotation encoding="application/x-tex">{\displaystyle E_{i}}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.515ex; height:2.509ex;" alt="{\displaystyle E_{i}}" loading="lazy"></span>.</li>
<li>Die Energien <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{i}}">
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<annotation encoding="application/x-tex">{\displaystyle E_{i}}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.515ex; height:2.509ex;" alt="{\displaystyle E_{i}}" loading="lazy"></span> sind <a href="Gau%C3%9F-Verteilung" class="mw-redirect" title="Gauß-Verteilung">gaußverteilt</a>.</li>
<li>Die Energien sind unabhängige Zufallsvariablen.</li></ul>
<p>Das Besondere am REM ist, dass es sich exakt lösen lässt, und sich trotz seiner Einfachheit wichtige Konzepte der statistischen Physik wie die eingefrorene Unordnung (<i>quenched disorder</i>), Replika-Symmetrie und Replika-Symmetrie-Brechung (RSB) an ihm studieren lassen. Betrachtet man ein REM-System in einem äußeren Magnetfeld, so findet man einen temperaturabhängigen <a href="Phasen%C3%BCbergang" title="Phasenübergang">Phasenübergang</a> zwischen einer eingefrorenen und einer <a href="Paramagnet" class="mw-redirect" title="Paramagnet">paramagnetischen</a> Phase.
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<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>
<ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Derrida <i>Random energy model: limit of a family of disordered models</i>, Phys. Rev. Lett., Bd. <b>45</b>, 1980, S. 79–82</span>
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<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Derrida: <i>Random energy model: an exactly solvable model of disordered systems</i>, Phys. Rev. B <b>24</b>, 2613-2326 (1981)</span>
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<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>
<ul><li>Anton Bovier <i>Statistical Mechanics of disordered systems - a mathematical perspective</i>, Cambridge University Press 2006</li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
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