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Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk

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Abstract

It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local,N-conserving elementary moves is nonergodic (hereN is the number of bonds in the walk). Indeed, for largeN, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Canada

    Neal Madras

  2. Department of Physics, New York University, 10003, New York, New York

    Alan D. Sokal

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  1. Neal Madras
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  2. Alan D. Sokal
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Madras, N., Sokal, A.D. Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk. J Stat Phys 47, 573–595 (1987). https://doi.org/10.1007/BF01007527

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  • DOI: https://doi.org/10.1007/BF01007527

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