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

Timothy M. Garoni, Giovanni Ossola, Marco Polin, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We study, via Monte Carlo simulation, 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 ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1. 25≤q≤4 in steps of 0. 25, on lattices up to 10242, and obtain estimates for the dynamic critical exponent zCM. We present evidence that when 1≤q≲1. 95 the Ossola-Sokal conjecture zCM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound zCM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.

    Original languageEnglish (US)
    Pages (from-to)459-518
    Number of pages60
    JournalJournal of Statistical Physics
    Volume144
    Issue number3
    DOIs
    StatePublished - Aug 2011

    Keywords

    • Chayes-Machta algorithm
    • Cluster algorithm
    • Dynamic critical behavior
    • Potts model
    • Random-cluster model
    • Swendsen-Wang algorithm

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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