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

Li, Bin; Sokal, Alan D.

doi:10.1007/BF01027299

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

Bin Li
(
- New York U.
)
,
Alan D. Sokal
(
- New York U.
)

1990

26 pages

Published in:

J.Statist.Phys. 61 (1990) 723-748

DOI:

10.1007/BF01027299

View in:

AMS MathSciNet

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Abstract: (Springer)

Let ζl be the critical exponent associated with the probability thatl independentN-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.

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