Some geometric critical exponents for percolation and the random-cluster model

Youjin Deng, Wei Zhang, Timothy M. Garoni, Alan D. Sokal, Andrea Sportiello

    Research output: Contribution to journalArticle

    Abstract

    We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension dmin in two dimensions: dmin =? (g+2) (g+18) / (32g), where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2cos (gπ/2) with 2≤g≤4.

    Original languageEnglish (US)
    Article number020102
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume81
    Issue number2
    DOIs
    StatePublished - Feb 10 2010

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

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