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| -rw-r--r-- | monte-carlo.tex | 11 |
1 files changed, 5 insertions, 6 deletions
diff --git a/monte-carlo.tex b/monte-carlo.tex index b24fa9d..2bc29ee 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -228,13 +228,12 @@ C\subset E$ is related to the probability of the reverse process $P(\set{s'}\to\ \[ \begin{aligned} \frac{P(\set s\to\set{s'})}{P(\set{s'}\to\set s)} - &=\frac{f_{\set s}(r\mid m_0)}{f_{\set s'}(r^{-1}\mid m_0)}\prod_{\{i,j\}\in + &=\frac{f_{m_0}(r\mid\set s)}{f_{m_0}(r^{-1}\mid\set s)}\prod_{\{i,j\}\in C}\frac{p_r(s_i,s_j)}{p_{r^{-1}}(s_i',s_j')}\prod_{\{i,j\}\in\partial - C}\frac{1-p_r(s_i,s_j)}{1-p_{r^{-1}}(s'_i,s'_j)}\\ - &=\prod_{\{i,j\}\in\partial - C}e^{\beta(\J(r\cdot s_i,s_j)-\J(s_i,s_j))} - =\frac{e^{-\beta\H(\set - s)}}{e^{-\beta\H(\set{s'})}}, + C}\frac{1-p_r(s_i,s_j)}{1-p_{r^{-1}}(s'_i,s'_j)} + =\prod_{\{i,j\}\in\partial + C}e^{\beta(\J(s_i',s_j')-\J(s_i,s_j))} + =\frac{e^{-\beta\H(\set{s'})}}{e^{-\beta\H(\set s)}}, \end{aligned} \] \end{widetext} |