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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2018-09-25 16:55:59 -0400 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2018-09-25 16:55:59 -0400 |
commit | 75423a60b13d8edcf4d05b6d8c3c55af33cf32a9 (patch) | |
tree | dfa192871a38ddad7fc25850def2572c61568a70 /monte-carlo.tex | |
parent | e6f638a736629a97f210b856fcded51a7ef09813 (diff) | |
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added discussion of the conserved order parameter tethered monte carlo that can produce results in a field
Diffstat (limited to 'monte-carlo.tex')
-rw-r--r-- | monte-carlo.tex | 25 |
1 files changed, 14 insertions, 11 deletions
diff --git a/monte-carlo.tex b/monte-carlo.tex index 4b9ba61..70cc952 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -89,17 +89,20 @@ extra degree of freedom, allowing the method to be used in a subcategory of interesting fields \cite{alexandrowicz_swendsen-wang_1989, wang_clusters_1989, ray_metastability_1990}. Static fields have also been applied by including a separate metropolis or heat bath update step after cluster formation -\cite{destri_swendsen-wang_1992, lauwers_critical_1989, ala-nissila_numerical_1994}, and other categories -of fields have been applied using replica methods -\cite{redner_graphical_1998,chayes_graphical_1998,machta_replica-exchange_2000}. -We show that the scaling of correlation time near the critical point of -several models suggests that the `ghost' approach is a natural one, e.g., that -it extends the celebrated scaling of dynamics in these algorithms at zero -field to various non-symmetric perturbations. We also show, by a redefinition -of the spin--spin coupling in a generic class of spin systems, -\emph{arbitrary} external fields can be treated using cluster methods. Rather -than the introduction of a `ghost spin,\!' our representation relies on -introducing a `ghost transformation.\!' +\cite{destri_swendsen-wang_1992, lauwers_critical_1989, +ala-nissila_numerical_1994}, and other categories of fields have been applied +using replica methods \cite{redner_graphical_1998, chayes_graphical_1998, +machta_replica-exchange_2000}. Monte Carlo techniques that involve cluster +updates at fixed magnetization have been used to examine quantities at fixed +field by integrating the associated thermodynamic functions +\cite{martin-mayor_cluster_2009, martin-mayor_tethered_2011}. We show that +the scaling of correlation time near the critical point of several models +suggests that the `ghost' approach is a natural one, e.g., that it extends the +celebrated scaling of dynamics in these algorithms at zero field to various +non-symmetric perturbations. We also show, by a redefinition of the spin--spin +coupling in a generic class of spin systems, \emph{arbitrary} external fields +can be treated using cluster methods. Rather than the introduction of a `ghost +spin,\!' our representation relies on introducing a `ghost transformation.\!' \section{Introduction} |