Garoni, Timothy M., Ossola, Giovanni, Polin, Marco and Sokal, Alan D. (2011) Dynamic critical behavior of the Chayes–Machta algorithm for the random-cluster model, I. two dimensions. Journal of Statistical Physics, Volume 144 (Number 3). pp. 459-518. doi:10.1007/s10955-011-0267-y

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Abstract

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 z CM. We present evidence that when 1≤q≲1.95 the Ossola–Sokal conjecture z CM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li–Sokal bound z CM≥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.

Item Type:	Journal Article
Divisions:	Faculty of Science > Physics
Journal or Publication Title:	Journal of Statistical Physics
Publisher:	Springer New York LLC
ISSN:	0022-4715
Official Date:	1 October 2011
Dates:	Date Event 1 October 2011 Published
Volume:	Volume 144
Number:	Number 3
Page Range:	pp. 459-518
DOI:	10.1007/s10955-011-0267-y
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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