Correction-to-scaling exponents for two-dimensional self-avoiding walks

Sergio Caracciolo, Anthony J. Guttmann, Iwan Jensen, Andrea Pelissetto, Andrew N. Rogers, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review


    We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ1=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.

    Original languageEnglish (US)
    Pages (from-to)1037-1100
    Number of pages64
    JournalJournal of Statistical Physics
    Issue number5-6
    StatePublished - Sep 2005


    • Conformal invariance
    • Corrections to scaling
    • Critical exponents
    • Exact enumeration
    • Monte Carlo
    • Pivot algorithm
    • Polymer
    • Self-avoiding walk
    • Series expansion

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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