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arXiv · 0705.2751

Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm

Youjin Deng·Timothy M. Garoni·Jonathan Machta·Giovanni Ossola·Marco Polin·Alan D. Sokal
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Abstract

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 \ge α/νis close to but probably not sharp in d=2, and is far from sharp in d=3, for all q. The conjecture z \ge β/νis false (for some values of q) in both d=2 and d=3.

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Youjin Deng, Timothy M. Garoni, Jonathan Machta, Giovanni Ossola, Marco Polin, Alan D. Sokal. 2007-05-18. Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm. https://doi.org/10.1103/physrevlett.99.055701

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