App_SourceCodes.tex

% !TeX root = Body.tex

\chapter{Simulation Algorithms}

\begin{algorithm}                      
	\caption{Single Flip Algorithm for a Monte Carlo Time (Equilibrium)}         
	\label{alg:SFAEMC}                          
	\begin{algorithmic}                  
	\FOR{$i_{\rm step} = 1, \dots, N_{\rm size}$}
	\STATE randomly chose a spin
	\STATE flip by the probability $\min\{1, \mathrm{e}^{\beta \Delta E}\}$
	\ENDFOR
	\STATE measurement
	\end{algorithmic}
\end{algorithm}

\begin{algorithm}                      
	\caption{Single Flip Algorithm for a Monte Carlo Time (Non-equilibrium)}         
	\label{alg:SFANEMC}                          
	\begin{algorithmic} 
		\STATE $\text{pump} = 0$  
		\STATE $\text{diss} = 0$                     
		\FOR {$i_{\rm v} = 1, \dots, v$}
			\STATE $\text{prev}\Leftarrow \text{energy on the slip plane}$
			\STATE sliding
			\STATE $\text{next}\Leftarrow \text{energy on the slip plane}$
			\STATE $\text{pump} = \text{pump} + (\text{next} - \text{prev})$
			\\
			\STATE $\text{prev}\Leftarrow \text{energy on the entire system}$
			\FOR{$i_{\rm step} = 1, \dots, N_{\rm size}/v$}
				\STATE flip by the probability $\min\{1, \mathrm{e}^{\beta \Delta E}\}$
			\ENDFOR
			\STATE $\text{next}\Leftarrow \text{energy on the entire system}$
			\STATE $\text{diss} = \text{diss} + (\text{next} - \text{prev})$
		\ENDFOR
		\STATE{measurement}
	\end{algorithmic}
\end{algorithm}