Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk

Neal Madras, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    Abstract

    It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local, N-conserving elementary moves is nonergodic (here N is the number of bonds in the walk). Indeed, for large N, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk.

    Original languageEnglish (US)
    Pages (from-to)573-595
    Number of pages23
    JournalJournal of Statistical Physics
    Volume47
    Issue number3-4
    DOIs
    StatePublished - May 1987

    Keywords

    • Monte Carlo
    • Self-avoiding walk
    • Verdier-Stockmayer
    • algorithm
    • ergodicity
    • lattice model
    • polymer

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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