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Critical exponent for the loop erased self-avoiding walk by Monte Carlo methods

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Abstract

A Monte Carlo simulation was performed for loop-erased self-avoiding walks (LESAW) to ascertain the exponentv for the Z2 and Z3 lattices. The estimated values were 2v=1.600±0.006 in two dimensions and 2v=1.232±0.008 in three dimensions, leading to the conjecturev=4/5 for the two-dimensional LESAW. These results add to existing evidence that the loop-erased self-avoiding walks are not in the same universality class as self-avoiding walks.

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Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, 3052, Parkville, Victoria, Australia

    A. J. Guttmann & R. J. Bursill

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  1. A. J. Guttmann
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  2. R. J. Bursill
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Guttmann, A.J., Bursill, R.J. Critical exponent for the loop erased self-avoiding walk by Monte Carlo methods. J Stat Phys 59, 1–9 (1990). https://doi.org/10.1007/BF01015560

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