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

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

2004-09-14

arxiv.org/abs/cond-mat/0409355v2

J.Statist.Phys.120:1037-1100,2005

Physics

Condensed Matter

Statistical Mechanics

LaTeX 2.09, 56 pages. Version 2 adds a renormalization-group discussion near the end of Section 2.2, and makes many small impr

Scientific paper

10.1007/s10955-005-7004-3

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 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.

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