Absence of mass gap for a class of stochastic contour models

Alan D. Sokal, Lawrence E. Thomas

    Research output: Contribution to journalArticle

    Abstract

    We study a class of Markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations. We show, under suitable hypotheses on the jump rates, that the infinitesimal generator has zero mass gap. This result covers (among others) the BFACF dynamics for fixed-endpoint self-avoiding walks and the Sterling-Greensite dynamics for fixed-boundary self-avoiding surfaces. Our models also mimic the Glauber dynamics for the low-temperature Ising model. The proofs are based on two new general principles: the minimum hitting-time argument and the mean (or mean-exponential) hitting-time argument.

    Original languageEnglish (US)
    Pages (from-to)907-947
    Number of pages41
    JournalJournal of Statistical Physics
    Volume51
    Issue number5-6
    DOIs
    StatePublished - Jun 1 1988

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    Keywords

    • Glauber dynamics
    • Markov chain
    • Markov process
    • Monte Carlo
    • contour model
    • dynamic critical phenomena
    • mass gap
    • self-avoiding walk

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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