New Monte Carlo method for the self-avoiding walk

Alberto Berretti, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find μ=2.63820 ± 0.00004 ± 0.00030 γ=1.352 ± 0.006 ± 0.025 νv=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length ≈ 166, using 340 hours CPU time on a CDC Cyber 170-730. We compare our results to previous work and indicate some directions for future research.

    Original languageEnglish (US)
    Pages (from-to)483-531
    Number of pages49
    JournalJournal of Statistical Physics
    Volume40
    Issue number3-4
    DOIs
    StatePublished - Aug 1985

    Fingerprint

    confidence limits
    Confidence Limits
    Self-avoiding Walk
    Monte Carlo method
    Corrections to Scaling
    Critical region
    Classical Limit
    Systematic Error
    Monte Carlo Algorithm
    CPU Time
    Square Lattice
    systematic errors
    scaling
    estimates
    Estimate

    Keywords

    • algorithm
    • critical exponents
    • lattice model
    • maximum-likelihood estimation
    • Monte Carlo
    • polymer
    • Self-avoiding walk

    ASJC Scopus subject areas

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

    Cite this

    New Monte Carlo method for the self-avoiding walk. / Berretti, Alberto; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 40, No. 3-4, 08.1985, p. 483-531.

    Research output: Contribution to journalArticle

    Berretti, Alberto ; Sokal, Alan D. / New Monte Carlo method for the self-avoiding walk. In: Journal of Statistical Physics. 1985 ; Vol. 40, No. 3-4. pp. 483-531.
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