Critical speeding-up in the local dynamics of the random-cluster model

Youjin Deng, Timothy M. Garoni, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We study the dynamic critical behavior of the local bond-update (Sweeny) dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2, 3 by Monte Carlo simulation. We show that, for a suitable range of q values, the global observable S2 exhibits "critical speeding-up": it decorrelates well on time scales much less than one sweep. In some cases the dynamic critical exponent for the integrated autocorrelation time is negative. We also show that the dynamic critical exponent zexp is very close (possibly equal) to the rigorous lower bound α/ν and quite possibly smaller than the corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.

    Original languageEnglish (US)
    Article number230602
    JournalPhysical Review Letters
    Volume98
    Issue number23
    DOIs
    StatePublished - Jun 7 2007

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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