From 20cb224511ca876d85378712827e54cd77cf9cc7 Mon Sep 17 00:00:00 2001
From: Janita Willumsen <j.willu@me.com>
Date: Thu, 9 Nov 2023 10:06:13 +0100
Subject: [PATCH] Move appendix file

---
 latex/ising_model.tex         |  4 ++--
 latex/sections/appendices.tex | 43 +++++++++++++++++++++++++++++++++++
 2 files changed, 45 insertions(+), 2 deletions(-)
 create mode 100644 latex/sections/appendices.tex

diff --git a/latex/ising_model.tex b/latex/ising_model.tex
index 1c4155e..be6820d 100644
--- a/latex/ising_model.tex
+++ b/latex/ising_model.tex
@@ -30,7 +30,7 @@
 \usepackage[noend]{algpseudocode}
 \usepackage{subfigure}
 \usepackage{tikz}
-% \usetikzlibrary{quantikz2}
+% \usetikzlibrary{quantikz}
 % defines the color of hyperref objects
 % Blending two colors:  blue!80!black  =  80% blue and 20% black
 \hypersetup{ % this is just my personal choice, feel free to change things
@@ -74,7 +74,7 @@
 \subfile{sections/conclusion}
 
 % Appendix
-\subfile{appendices}
+\subfile{sections/appendices}
 
 \onecolumngrid
 
diff --git a/latex/sections/appendices.tex b/latex/sections/appendices.tex
new file mode 100644
index 0000000..3525403
--- /dev/null
+++ b/latex/sections/appendices.tex
@@ -0,0 +1,43 @@
+\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