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Dimitri Lozeve 2020-07-20 10:38:39 +02:00
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_site/posts/ising-model.html
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</section>
<section>
<p>The <a href="https://en.wikipedia.org/wiki/Ising_model">Ising model</a> is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.</p>
<h2>Table of Contents</h2><ul>
<li><a href="#mathematical-definition">Mathematical definition</a></li>
<li><a href="#simulation">Simulation</a></li>
<li><a href="#implementation">Implementation</a></li>
<li><a href="#conclusion">Conclusion</a></li>
</ul>
<p>The <a href="https://en.wikipedia.org/wiki/Ising_model">Ising model</a> is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.</p>
<p><img src="../images/ising.gif" /></p>
<h2 id="mathematical-definition">Mathematical definition</h2>
<p>We have a lattice <span class="math inline">\(\Lambda\)</span> consisting of sites <span class="math inline">\(k\)</span>. For each site, there is a moment <span class="math inline">\(\sigma_k \in \{ -1, +1 \}\)</span>. <span class="math inline">\(\sigma =