From 2b35ab592fb0197d515f9534095077b5ed4437a3 Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Thu, 9 Nov 2023 10:07:26 +0100 Subject: [PATCH] Move file --- latex/appendices.tex | 43 ------------------------------------------- 1 file changed, 43 deletions(-) delete mode 100644 latex/appendices.tex diff --git a/latex/appendices.tex b/latex/appendices.tex deleted file mode 100644 index 3525403..0000000 --- a/latex/appendices.tex +++ /dev/null @@ -1,43 +0,0 @@ -\documentclass[../ising_model.tex]{subfiles} - -\begin{document} -\appendix -\section{Ising model system states}\label{sec:system_states} -To avoid counting duplicates, we used -\begin{figure}\label{fig:tikz_counting} - \centering - \begin{tikzpicture} - \draw (0, 0) grid (2, 2); - % \node[inner] (s1) at (0.5, 0.5) {s}; - \node (s1) at (0.5, 1.5) {$s_1$}; - \node (s2) at (1.5, 1.5) {$s_2$}; - \node (s3) at (0.5, 0.5) {$s_3$}; - \node (s4) at (1.5, 0.5) {$s_4$}; - \node[gray] (s12) at (2.5, 1.5) {$s_1$}; - \node[gray] (s34) at (2.5, 0.5) {$s_3$}; - \node[gray] (s13) at (0.5, -0.5) {$s_1$}; - \node[gray] (s24) at (1.5, -0.5) {$s_2$}; - - \draw[red, ->] (s1.east) -- (s2.west); - \draw[red, ->] (s2.east) -- (s12.west); - \draw[red, ->] (s1.south) -- (s3.north); - \draw[red, ->] (s2.south) -- (s4.north); - \draw[red, ->] (s3.east) -- (s4.west); - \draw[red, ->] (s4.east) -- (s34.west); - \draw[red, ->] (s3.south) -- (s13.north); - \draw[red, ->] (s4.south) -- (s24.north); - \end{tikzpicture} - \caption{Rules for multiplying spin pairs.} -\end{figure} - - -\section{Analytical expressions}\label{sec:analytical_expressions} -The Boltzmann distribution is normalized using a partition function $Z$ given by -\begin{align*} - Z &= \sum_{\text{all possible } s_{i}}^{N} e^{-\beta E(\mathbf{s})} \\ - &= \dots \\ - &= 4 \cosh (8 \beta J) + 12 \\ -\end{align*} - - -\end{document} \ No newline at end of file