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Move appendix file

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Janita Willumsen 2023-11-09 10:06:13 +01:00
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2 changed files with 45 additions and 2 deletions
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4
latex/ising_model.tex
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@ -30,7 +30,7 @@
\usepackage[noend]{algpseudocode} \usepackage[noend]{algpseudocode}
\usepackage{subfigure} \usepackage{subfigure}
\usepackage{tikz} \usepackage{tikz}
% \usetikzlibrary{quantikz2} % \usetikzlibrary{quantikz}
% defines the color of hyperref objects % defines the color of hyperref objects
% Blending two colors: blue!80!black = 80% blue and 20% black % Blending two colors: blue!80!black = 80% blue and 20% black
\hypersetup{ % this is just my personal choice, feel free to change things \hypersetup{ % this is just my personal choice, feel free to change things
@ -74,7 +74,7 @@
\subfile{sections/conclusion} \subfile{sections/conclusion}
% Appendix % Appendix
\subfile{appendices} \subfile{sections/appendices}
\onecolumngrid \onecolumngrid

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latex/sections/appendices.tex Normal file
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\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}