Critical speeding-up in a local dynamics for the random-cluster model

Abstract

We study the dynamic critical behavior of the local bond-update (Sweeny) dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2,3, by Monte Carlo simulation. We show that, for a suitable range of q values, the global observable S_2 exhibits "critical speeding-up": it decorrelates well on time scales much less than one sweep, so that the integrated autocorrelation time tends to zero as the critical point is approached. We also show that the dynamic critical exponent z_{exp} is very close (possibly equal) to the rigorous lower bound \alpha/\nu, and quite possibly smaller than the corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.