Deng, YGaroni, TMachta, JOssola, GPolin, MSokal, A2024-04-262024-04-262007-01https://hdl.handle.net/20.500.14394/40493This is the prepublished version harvested from ArXiv. The published version is located at http://prl.aps.org/abstract/PRL/v99/i5/e055701We 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.Physicsarticle