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authorJaron Kent-Dobias <jaron@kent-dobias.com>2018-09-25 00:22:28 -0400
committerJaron Kent-Dobias <jaron@kent-dobias.com>2018-09-25 00:22:28 -0400
commit7fe4545d9aa22abc9a7b2b8486f033cac2cec041 (patch)
tree372f8192d9f991784a28436e87dfe7873a557f4b
parent3ef6f5a006865c6ea87455bd698d5d2aa7b3f46f (diff)
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spacing tweak on detailed balance equation
-rw-r--r--monte-carlo.tex2
1 files changed, 1 insertions, 1 deletions
diff --git a/monte-carlo.tex b/monte-carlo.tex
index 2bc29ee..a3e18a4 100644
--- a/monte-carlo.tex
+++ b/monte-carlo.tex
@@ -231,7 +231,7 @@ C\subset E$ is related to the probability of the reverse process $P(\set{s'}\to\
&=\frac{f_{m_0}(r\mid\set s)}{f_{m_0}(r^{-1}\mid\set s)}\prod_{\{i,j\}\in
C}\frac{p_r(s_i,s_j)}{p_{r^{-1}}(s_i',s_j')}\prod_{\{i,j\}\in\partial
C}\frac{1-p_r(s_i,s_j)}{1-p_{r^{-1}}(s'_i,s'_j)}
- =\prod_{\{i,j\}\in\partial
+ =\!\!\!\!\prod_{\{i,j\}\in\partial
C}e^{\beta(\J(s_i',s_j')-\J(s_i,s_j))}
=\frac{e^{-\beta\H(\set{s'})}}{e^{-\beta\H(\set s)}},
\end{aligned}