Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions

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 \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95 the Ossola-Sokal conjecture z_{CM} \ge β/νis violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z_{CM} \ge α/νis close to being sharp over the entire range 1 \le q \le 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.

LaTeX2e, 75 pages including 26 Postscript figures

References in corpus (3)

• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• The self-dual point of the two-dimensional random-cluster model is critical for $q\ge 1$
• Percolation transitions in two dimensions

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• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations
• On the CFT describing the spin clusters in 2d Potts model
• On the coupling time of the heat-bath process for the Fortuin-Kasteleyn random-cluster model