High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Bin Li, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.

    Original languageEnglish (US)
    Pages (from-to)723-748
    Number of pages26
    JournalJournal of Statistical Physics
    Volume61
    Issue number3-4
    DOIs
    StatePublished - Nov 1990

    Keywords

    • Monte Carlo
    • conformal invariance
    • maximum-likelihood estimation
    • mutually-avoiding walks
    • random walk
    • self-avoiding walk

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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