TY - JOUR
T1 - Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model, I. Two Dimensions
AU - Garoni, Timothy M.
AU - Ossola, Giovanni
AU - Polin, Marco
AU - Sokal, Alan D.
N1 - Funding Information:
This research was supported in part by U.S. National Science Foundation grants PHY-0116590 and PHY-0424082. It was also supported under the Australian Research Council’s Discovery Projects funding scheme (project number DP110101141); and T.G. is the recipient of an Australian Research Council Future Fellowship (project number FT100100494).
PY - 2011/8
Y1 - 2011/8
N2 - We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1. 25≤q≤4 in steps of 0. 25, on lattices up to 10242, and obtain estimates for the dynamic critical exponent zCM. We present evidence that when 1≤q≲1. 95 the Ossola-Sokal conjecture zCM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound zCM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.
AB - We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1. 25≤q≤4 in steps of 0. 25, on lattices up to 10242, and obtain estimates for the dynamic critical exponent zCM. We present evidence that when 1≤q≲1. 95 the Ossola-Sokal conjecture zCM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound zCM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.
KW - Chayes-Machta algorithm
KW - Cluster algorithm
KW - Dynamic critical behavior
KW - Potts model
KW - Random-cluster model
KW - Swendsen-Wang algorithm
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U2 - 10.1007/s10955-011-0267-y
DO - 10.1007/s10955-011-0267-y
M3 - Article
AN - SCOPUS:80052032136
SN - 0022-4715
VL - 144
SP - 459
EP - 518
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3
ER -