Add section headings to all files, and add analytical values for problem 1

latex/ising_model.tex

@@ -30,7 +30,7 @@
 \usepackage[noend]{algpseudocode}
 \usepackage{subfigure}
 \usepackage{tikz}
-\usetikzlibrary{quantikz2}
+% \usetikzlibrary{quantikz2}
 % 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
@@ -49,7 +49,7 @@
 
 \begin{document}
 
-\title{Project 3}  % self-explanatory
+\title{Project 4}  % self-explanatory
 \author{Cory Alexander Balaton \& Janita Ovidie Sandtrøen Willumsen \\ \faGithub \, \url{https://github.uio.no/FYS3150-G2-2023/Project-4}} % self-explanatory
 \date{\today}                             % self-explanatory
 \noaffiliation                            % ignore this, but keep it.

latex/references.bib

@@ -67,8 +67,3 @@
 }
 
 # Miscellaneous things
-@misc{penning:fig,
-    key = {something},
-    url = {https://www.med.physik.uni-muenchen.de/research/nuclear-science/nuclear-masses/mlltrap/layout/traps/index.html},
-    note = {Configuration figure a}
-}

latex/sections/abstract.tex

@@ -1,4 +1,7 @@
 \documentclass[../ising_model.tex]{subfiles}
 
 \begin{document}
+\begin{abstract}
+	We did some amazing stuff!
+\end{abstract}
 \end{document}

latex/sections/conclusion.tex

@@ -1,4 +1,6 @@
 \documentclass[../ising_model.tex]{subfiles}
 
 \begin{document}
+\section{Conclusion}\label{sec:conclusion}
+
 \end{document}

latex/sections/introduction.tex

@@ -1,7 +1,7 @@
 \documentclass[../ising_model.tex]{subfiles}
 
 \begin{document}
-
+\section{Introduction}\label{sec:introduction}
 \cite{openmp:2018}
 
 \end{document}

latex/sections/methods.tex

@@ -1,5 +1,60 @@
 \documentclass[../ising_model.tex]{subfiles}
 
 \begin{document}
+\section{Methods}\label{sec:methods}
+% Problem 1
+\begin{align*}
+	Z &= \sum_{all \ s_{i}}^{N} e^{-\beta E(\mathbf{s})} \\
+	&= \dots \\
+	&= 4 \cosh (8 \beta J) + 12 \\
+\end{align*}
+%
+\begin{align*}
+	\langle \epsilon \rangle &= \frac{-2J \sinh(8 \beta J)}{ \cosh(8 \beta J) + 3}
+\end{align*}
+%
+\begin{align*}
+	\langle \epsilon^{2} \rangle &= \frac{4 J^{2} \cosh(8 \beta J)}{\cosh(8 \beta J) + 3}
+\end{align*}
+%
+\begin{align*}
+	\langle |m| \rangle &= \frac{e^{8 \beta J} + 1}{2( \cosh(8 \beta J) + 3)}
+\end{align*}
+\begin{align*}
+	\langle |m|^{2} \rangle &= \frac{e^{8 \beta J} + 1}{2( \cosh(8 \beta J) + 3)}
+\end{align*}
+%
+\begin{align*}
+	\langle E \rangle &= \frac{-8 J \sinh(8 \beta J)}{\cosh(8 \beta J) + 3} 
+\end{align*}
+%
+\begin{align*}
+	\langle E \rangle^{2} &= \frac{64 J^{2} \sinh(8 \beta J)}{(\cosh(8 \beta J) + 3)^{2}}
+\end{align*}
+%
+\begin{align*}
+	\langle E^{2} \rangle &= \frac{64 J^{2} \cosh(8 \beta J)}{\cosh(8 \beta J) + 3}
+\end{align*}
+%
+\begin{align*}
+	\langle M \rangle &= \frac{2 e^{8 \beta J}}{\cosh(8 \beta J) + 3}
+\end{align*}
+%
+\begin{align*}
+	\langle M \rangle^{2} &= \frac{4e^{16 \beta J} +  16e^{8 \beta J} + 16}{(\cosh(8 \beta J) + 3)^{2}}
+\end{align*}
+%
+\begin{align*}
+	\langle M^{2} \rangle &= \frac{8e^{8 \beta J} +  8}{\cosh(8 \beta J) + 3}
+\end{align*}
+%
+\begin{align*}
+	C_{V} &= \frac{64 J^{2}}{N k_{\text{B}} T^{2}} \Big( \frac{3 \cosh(8 \beta J) + \cosh^{2}(8 \beta J) - \sinh^{2}(8 \beta J)}{(\cosh(8 \beta J) + 3)^{2}} \Big)
+\end{align*}
+%
+\begin{align*}
+	\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)
+\end{align*}
 \end{document}
 

latex/sections/results.tex

@@ -1,4 +1,6 @@
 \documentclass[../ising_model.tex]{subfiles}
 
 \begin{document}
+\section{Results}\label{sec:results}
+
 \end{document}