New Monte Carlo method for the self-avoiding walk

Alberto Berretti, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number3-4
    StatePublished - Aug 1985


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

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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