added discussion of the conserved order parameter tethered monte carlo that can produce results in a field

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}