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 journalArticle

    Abstract

    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
    Volume120
    Issue number5-6
    DOIs
    StatePublished - Sep 2005

    Fingerprint

    Corrections to Scaling
    Self-avoiding Walk
    Scaling Exponent
    Mean Square
    exponents
    scaling
    Square Lattice
    pivots
    radii
    Radius
    gyration
    cancellation
    Pivot
    Triangular Lattice
    Monte Carlo method
    Conformal Field Theory
    extrapolation
    Cancellation
    Extrapolation
    monomers

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

    Caracciolo, S., Guttmann, A. J., Jensen, I., Pelissetto, A., Rogers, A. N., & Sokal, A. D. (2005). Correction-to-scaling exponents for two-dimensional self-avoiding walks. Journal of Statistical Physics, 120(5-6), 1037-1100. https://doi.org/10.1007/s10955-005-7004-3

    Correction-to-scaling exponents for two-dimensional self-avoiding walks. / Caracciolo, Sergio; Guttmann, Anthony J.; Jensen, Iwan; Pelissetto, Andrea; Rogers, Andrew N.; Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 120, No. 5-6, 09.2005, p. 1037-1100.

    Research output: Contribution to journalArticle

    Caracciolo, S, Guttmann, AJ, Jensen, I, Pelissetto, A, Rogers, AN & Sokal, AD 2005, 'Correction-to-scaling exponents for two-dimensional self-avoiding walks', Journal of Statistical Physics, vol. 120, no. 5-6, pp. 1037-1100. https://doi.org/10.1007/s10955-005-7004-3
    Caracciolo S, Guttmann AJ, Jensen I, Pelissetto A, Rogers AN, Sokal AD. Correction-to-scaling exponents for two-dimensional self-avoiding walks. Journal of Statistical Physics. 2005 Sep;120(5-6):1037-1100. https://doi.org/10.1007/s10955-005-7004-3
    Caracciolo, Sergio ; Guttmann, Anthony J. ; Jensen, Iwan ; Pelissetto, Andrea ; Rogers, Andrew N. ; Sokal, Alan D. / Correction-to-scaling exponents for two-dimensional self-avoiding walks. In: Journal of Statistical Physics. 2005 ; Vol. 120, No. 5-6. pp. 1037-1100.
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