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diff --git a/monte-carlo.tex b/monte-carlo.tex index 96942da..a26fd50 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -245,6 +245,14 @@ reverse process $P(\set{s'}\to\set s)$ by whence detailed balance is also satisfied, using $r=r^{-1}$ and $Z(r\cdot s',s')=Z(r\cdot s,s)$. +The Wolff algorithm is well known to be efficient in sampling many spin models +near and away from criticality, including the Ising, Potts, and $\mathrm O(n)$ +models. In general, its efficiently will depend on the system at hand, e.g., +the structure of the configurations $X$ and group $R$. A detailed discussion +of this dependence for a class of configuration spaces with continuous +symmetry groups can be found in \cite{caracciolo_generalized_1991, +caracciolo_wolff-type_1993}. + \section{Adding the field} This algorithm relies on the fact that the coupling $\J$ depends only on |