diff --git a/latex/sections/methods.tex b/latex/sections/methods.tex index 3178903..64ed8b4 100644 --- a/latex/sections/methods.tex +++ b/latex/sections/methods.tex @@ -2,6 +2,7 @@ \begin{document} \section{Methods}\label{sec:methods} +\subsection{The Ising model}\label{sec:ising} % Problem 1 \begin{align*} Z &= \sum_{all \ s_{i}}^{N} e^{-\beta E(\mathbf{s})} \\ @@ -56,5 +57,12 @@ \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*} + +\subsection{Markov Chain Monte Carlo methods} + + +\subsection{Implementation} + + \end{document}