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We study, via Monte Carlo simulation, the dynamic critical behavior of theChayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, whichgeneralizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet tonon-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 insteps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamiccritical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we alsopresent plausible fits compatible with this conjecture. We show that theLi-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entirerange 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct ofour work, we also obtain evidence concerning the corrections to scaling instatic observables.

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