Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints

Sergio Caracciolo, Andrea Pelissetto, AJan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of steps Ntot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel "join- and-cut" move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N≈1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent γ.

    Original languageEnglish (US)
    Pages (from-to)65-111
    Number of pages47
    JournalJournal of Statistical Physics
    Volume67
    Issue number1-2
    DOIs
    StatePublished - Apr 1992

    Fingerprint

    Self-avoiding Walk
    Join
    Walk
    heuristic methods
    Pivot
    Monte Carlo Algorithm
    Heuristic Method
    pivots
    Critical Behavior
    Autocorrelation
    Critical Exponents
    Dynamic Behavior
    Higher Dimensions
    Two Dimensions
    Ensemble
    Numerical Methods
    autocorrelation
    Unit
    exponents

    Keywords

    • critical exponent
    • join- and-cut algorithm
    • Monte Carlo
    • pivot algorithm
    • polymer
    • Self-avoiding walk

    ASJC Scopus subject areas

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

    Cite this

    Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints. / Caracciolo, Sergio; Pelissetto, Andrea; Sokal, AJan D.

    In: Journal of Statistical Physics, Vol. 67, No. 1-2, 04.1992, p. 65-111.

    Research output: Contribution to journalArticle

    Caracciolo, Sergio ; Pelissetto, Andrea ; Sokal, AJan D. / Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints. In: Journal of Statistical Physics. 1992 ; Vol. 67, No. 1-2. pp. 65-111.
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