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

Neal Madras, Alan D. Sokal

    Research output: Contribution to journalArticle

    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

    Fingerprint

    Self-avoiding Walk
    Monte Carlo Algorithm
    Dynamic Algorithms
    Monte Carlo Study
    Walk
    Generalization
    Class
    Form

    Keywords

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

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Physics and Astronomy(all)
    • Mathematical Physics

    Cite this

    Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk. / Madras, Neal; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 47, No. 3-4, 05.1987, p. 573-595.

    Research output: Contribution to journalArticle

    @article{8fc0bcb626f14d83b477b0b9d5232d88,
    title = "Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk",
    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.",
    keywords = "algorithm, ergodicity, lattice model, Monte Carlo, polymer, Self-avoiding walk, Verdier-Stockmayer",
    author = "Neal Madras and Sokal, {Alan D.}",
    year = "1987",
    month = "5",
    doi = "10.1007/BF01007527",
    language = "English (US)",
    volume = "47",
    pages = "573--595",
    journal = "Journal of Statistical Physics",
    issn = "0022-4715",
    publisher = "Springer New York",
    number = "3-4",

    }

    TY - JOUR

    T1 - Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk

    AU - Madras, Neal

    AU - Sokal, Alan D.

    PY - 1987/5

    Y1 - 1987/5

    N2 - 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.

    AB - 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.

    KW - algorithm

    KW - ergodicity

    KW - lattice model

    KW - Monte Carlo

    KW - polymer

    KW - Self-avoiding walk

    KW - Verdier-Stockmayer

    UR - http://www.scopus.com/inward/record.url?scp=34250103739&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=34250103739&partnerID=8YFLogxK

    U2 - 10.1007/BF01007527

    DO - 10.1007/BF01007527

    M3 - Article

    VL - 47

    SP - 573

    EP - 595

    JO - Journal of Statistical Physics

    JF - Journal of Statistical Physics

    SN - 0022-4715

    IS - 3-4

    ER -