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Update section layout

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Janita Willumsen 2023-11-09 08:16:16 +01:00
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latex/sections/methods.tex
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@ -2,6 +2,7 @@
\begin{document} \begin{document}
\section{Methods}\label{sec:methods} \section{Methods}\label{sec:methods}
\subsection{The Ising model}\label{sec:ising}
% Problem 1 % Problem 1
\begin{align*} \begin{align*}
Z &= \sum_{all \ s_{i}}^{N} e^{-\beta E(\mathbf{s})} \\ Z &= \sum_{all \ s_{i}}^{N} e^{-\beta E(\mathbf{s})} \\
@ -56,5 +57,12 @@
\chi &= \frac{1}{N} \frac{1}{k_{\text{B}} T^{2}} (\langle M^{2} \rangle - \langle M \rangle^{2}) \\ \chi &= \frac{1}{N} \frac{1}{k_{\text{B}} T^{2}} (\langle M^{2} \rangle - \langle M \rangle^{2}) \\
&= \frac{1}{N k_{\text{B}} T} \Big( \frac{12e^{8 \beta J} + 4 e^{-8 \beta J} + 12}{(\cosh(8 \beta J) + 3)^{2}} \Big) &= \frac{1}{N k_{\text{B}} T} \Big( \frac{12e^{8 \beta J} + 4 e^{-8 \beta J} + 12}{(\cosh(8 \beta J) + 3)^{2}} \Big)
\end{align*} \end{align*}
\subsection{Markov Chain Monte Carlo methods}
\subsection{Implementation}
\end{document} \end{document}