High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Bin Li; Alan D. Sokal

doi:10.1007/BF01027299

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Bin Li, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

Let ζ_l be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ₂=0.6240±0.0005±0.0011 and ζ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ₂=5/8 and ζ₃=35/24.

Original language	English (US)
Pages (from-to)	723-748
Number of pages	26
Journal	Journal of Statistical Physics
Volume	61
Issue number	3-4
DOIs	https://doi.org/10.1007/BF01027299
State	Published - Nov 1990

Keywords

Monte Carlo
conformal invariance
maximum-likelihood estimation
mutually-avoiding walks
random walk
self-avoiding walk

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01027299

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title = "High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks",

abstract = "Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.",

keywords = "Monte Carlo, conformal invariance, maximum-likelihood estimation, mutually-avoiding walks, random walk, self-avoiding walk",

author = "Bin Li and Sokal, {Alan D.}",

year = "1990",

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T1 - High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

AU - Li, Bin

AU - Sokal, Alan D.

PY - 1990/11

Y1 - 1990/11

N2 - Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.

AB - Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.

KW - Monte Carlo

KW - conformal invariance

KW - maximum-likelihood estimation

KW - mutually-avoiding walks

KW - random walk

KW - self-avoiding walk

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ER -

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

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Keywords

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