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 approximate 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 Delta(1)=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.

Correction-to-scaling exponents for two-dimensional self-avoiding walks / S. Caracciolo, A.J. Guttmann, I. Jensen, A. Pelissetto, A.N. Rogers, A.D. Sokal. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 120:5-6(2005), pp. 1037-1100.

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

S. Caracciolo;
2005

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 approximate 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 Delta(1)=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.
self-avoiding walk; polymer; exact enumeration; series expansion; Monte Carlo; pivot algorithm; corrections to scaling; critical exponents; conformal invariance
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
JOURNAL OF STATISTICAL PHYSICS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/9715
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