Critical Behavior of the Chayes–Machta–Swendsen–Wang Dynamics

We study 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 model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z≥α/ν is close to but probably not sharp in d=2 and is far from sharp in d=3, for all q. The conjecture z≥β/ν is false (for some values of q) in both d=2 and d=3