Correction-to-Scaling Exponents for Two-Dimensional Self-Avoiding Walks |
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Authors: | Sergio Caracciolo Anthony J Guttmann Iwan Jensen Andrea Pelissetto Andrew N Rogers Alan D Sokal |
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Institution: | (1) Dip. di Fisica and INFN, Università di Milano, via Celoria 16, I-20133 Milano, Italy;(2) Department of Mathematics and Statistics, University of Melbourne, Vic., 3010, Australia;(3) Dip. di Fisica and INFN–Sezione di Roma I, Università di Roma I, I-00185 Roma, Italy;(4) Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA |
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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. |
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Keywords: | Self-avoiding walk polymer exact enumeration series expansion Monte Carlo pivot algorithm corrections to scaling critical exponents conformal invariance |
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