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

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Abstract

Let ζ l 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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  1. Department of Physics, New York University, 10003, New York, New York

    Bin Li & Alan D. Sokal

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  1. Bin Li
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  2. Alan D. Sokal
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Li, B., Sokal, A.D. High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks. J Stat Phys 61, 723–748 (1990). https://doi.org/10.1007/BF01027299

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