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 journalArticle

    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

    Fingerprint

    Monte Carlo Test
    Walk
    invariance
    Invariance
    confidence limits
    Confidence Limits
    Prediction
    predictions
    Corrections to Scaling
    Conformal Invariance
    Classical Limit
    Systematic Error
    random walk
    systematic errors
    Monte Carlo method
    Critical Exponents
    Maximum Likelihood
    Random walk
    Data analysis
    Two Dimensions

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

    High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks. / Li, Bin; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 61, No. 3-4, 11.1990, p. 723-748.

    Research output: Contribution to journalArticle

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