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


    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
    Issue number1-2
    StatePublished - Apr 1992


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

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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