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

    Fingerprint

    Random-cluster Model
    Critical Behavior
    Dynamic Behavior
    Two Dimensions
    Corrections to Scaling
    Ferromagnet
    Critical Exponents
    Monte Carlo Simulation
    Entire
    Generalise
    exponents
    scaling
    Estimate
    Range of data
    estimates
    Evidence
    simulation

    Keywords

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

    ASJC Scopus subject areas

    • Mathematical Physics
    • Statistical and Nonlinear Physics

    Cite this

    Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model, I. Two Dimensions. / Garoni, Timothy M.; Ossola, Giovanni; Polin, Marco; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 144, No. 3, 08.2011, p. 459-518.

    Research output: Contribution to journalArticle

    Garoni, Timothy M. ; Ossola, Giovanni ; Polin, Marco ; Sokal, Alan D. / Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model, I. Two Dimensions. In: Journal of Statistical Physics. 2011 ; Vol. 144, No. 3. pp. 459-518.
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