New lower bounds on the self-avoiding-walk connective constant

Takashi Hara, Gordon Slade, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice ℤd. The method is based on loop erasure and restoration, and does not require exact enumeration data. Our bounds are best for high d, and in fact agree with the first four terms of the 1/d expansion for the connective constant. The bounds are the best to date for dimensions d≥ 3, but do not produce good results in two dimensions. For d=3, 4, 5, and 6, respectively, our lower bound is within 2.4%, 0.43%, 0.12%, and 0.044% of the value estimated by series extrapolation.

    Original languageEnglish (US)
    Pages (from-to)479-517
    Number of pages39
    JournalJournal of Statistical Physics
    Volume72
    Issue number3-4
    DOIs
    StatePublished - Aug 1993

    Fingerprint

    Self-avoiding Walk
    Lower bound
    Exact Enumeration
    enumeration
    Restoration
    Extrapolation
    restoration
    extrapolation
    Two Dimensions
    expansion
    Series
    Term

    Keywords

    • 1/d expansion
    • connective constant
    • loop erasure
    • random walk
    • Self-avoiding walk

    ASJC Scopus subject areas

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

    Cite this

    New lower bounds on the self-avoiding-walk connective constant. / Hara, Takashi; Slade, Gordon; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 72, No. 3-4, 08.1993, p. 479-517.

    Research output: Contribution to journalArticle

    Hara, Takashi ; Slade, Gordon ; Sokal, Alan D. / New lower bounds on the self-avoiding-walk connective constant. In: Journal of Statistical Physics. 1993 ; Vol. 72, No. 3-4. pp. 479-517.
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