Critical behavior of the Chayes-Machta-Swendsen-Wang dynamics

Youjin Deng; Timothy M. Garoni; Jonathan MacHta; Giovanni Ossola; Marco Polin; Alan D. Sokal

doi:10.1103/PhysRevLett.99.055701

Critical behavior of the Chayes-Machta-Swendsen-Wang dynamics

Youjin Deng, Timothy M. Garoni, Jonathan MacHta, Giovanni Ossola, Marco Polin, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

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 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 zβ/ν is false (for some values of q) in both d=2 and d=3.

Original language	English (US)
Article number	055701
Journal	Physical Review Letters
Volume	99
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevLett.99.055701
State	Published - Jul 31 2007

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General Physics and Astronomy

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10.1103/PhysRevLett.99.055701

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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 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 zβ/ν is false (for some values of q) in both d=2 and d=3.",

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AU - Ossola, Giovanni

AU - Polin, Marco

AU - Sokal, Alan D.

PY - 2007/7/31

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AB - 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 zβ/ν is false (for some values of q) in both d=2 and d=3.

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Critical behavior of the Chayes-Machta-Swendsen-Wang dynamics

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