\documentclass[../ising_model.tex]{subfiles}

\begin{document}
\section{Results}\label{sec:results}

\subsection{Draft}
Test that the numerical stuff gets close to the analytical 
- validate implementation a given number of times, find average number of cycles

Initial state ordered vs random
- start ordered both at up=1 and random 

burn-in time
- burn-in 5000 vs 10000 mc cycles, only mention how a longer burn-in time can in some cases result in better cv and x

probability using histogram of samples
- Comparing the histogram of $T_1 = 1.0$ and $T_2 = 2.4$. For $T_1 = 1.0$ we see a lower acceptance of flips, resulting in a low variance. The histogram looks more like an exponential function

parallelization
- temp mpi
- each mpi process spawn thread that make own ising model
- each ising model goes through burn in time (no benefit)
- sampling done in parallel
- mcmc sampling openmp

phase transition
critical temperature
\end{document}