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 ferr...
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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 1024(2), and obtain estimates for the dynamic critical exponent z(CM). We present evidence that when 1 <= q less than or similar to 1.95 the Ossola-Sokal conjecture z(CM) = >= beta/nu is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z(CM) >= alpha/nu 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.
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