diff --git a/latex/ising_model.tex b/latex/ising_model.tex index 2614b7d..3a0d6f2 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{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. diff --git a/latex/references.bib b/latex/references.bib index d1dfe6c..494f104 100644 --- a/latex/references.bib +++ b/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} -} diff --git a/latex/sections/abstract.tex b/latex/sections/abstract.tex index b05e0b6..b69617c 100644 --- a/latex/sections/abstract.tex +++ b/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} diff --git a/latex/sections/conclusion.tex b/latex/sections/conclusion.tex index b05e0b6..073c2e9 100644 --- a/latex/sections/conclusion.tex +++ b/latex/sections/conclusion.tex @@ -1,4 +1,6 @@ \documentclass[../ising_model.tex]{subfiles} \begin{document} +\section{Conclusion}\label{sec:conclusion} + \end{document} diff --git a/latex/sections/introduction.tex b/latex/sections/introduction.tex index 7322a58..62d86ae 100644 --- a/latex/sections/introduction.tex +++ b/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} diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex index 81ddfcc..3178903 100644 --- a/latex/sections/methods.tex +++ b/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} diff --git a/latex/sections/results.tex b/latex/sections/results.tex index b05e0b6..26924a0 100644 --- a/latex/sections/results.tex +++ b/latex/sections/results.tex @@ -1,4 +1,6 @@ \documentclass[../ising_model.tex]{subfiles} \begin{document} +\section{Results}\label{sec:results} + \end{document}