Add algorithm for the Metropolis algorithm

2023-11-26 19:18:26 +01:00 · 2023-11-26 19:18:26 +01:00 · b5eadd2e56
commit b5eadd2e56
parent 4086e30f6f
1 changed files with 23 additions and 0 deletions
--- a/latex/metropolis.tex
+++ b/latex/metropolis.tex
@ -0,0 +1,23 @@
+\begin{figure}[H]
+    \begin{algorithm}[H]
+    \caption{Metropolis-Hastings Algorithm}
+    \label{algo:metropolis}
+        \begin{algorithmic}
+            \Procedure{Metropolis}{$lattice, energy, magnetization$}
+            \For{ Each spin in the lattice }
+            \State $ri \leftarrow \text{random index of the lattice}$
+            \State $rj \leftarrow \text{random index of the lattice}$
+            \State $dE \leftarrow 2 \cdot lattice_{ri,rj} \cdot (lattice_{ri,rj-1} + lattice_{ri,rj+1} 
+            + lattice_{ri-1,rj} + lattice_{ri+1,rj} )$
+
+            \State $rn \leftarrow \text{random number} \in [0,1)$
+            \If{$rn \leq e^{- \frac{dE}{T}}$}
+                \State $lattice_{ri,rj} = -1 \cdot lattice_{ri,rj}$
+                \State $magnetization = magnetization + 2 \cdot lattice_{ri,rj}$
+                \State $energy = energy + dE$
+            \EndIf
+            \EndFor
+            \EndProcedure
+        \end{algorithmic}
+    \end{algorithm}
+\end{figure}