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Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints

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Abstract

We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of stepsN tot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel “join- and-cut” move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N≈1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponentγ.

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Author notes

  1. Andrea Pelissetto

    Present address: Dipartimento di Fisica, Università degli Studi di Pisa, 56100, Pisa, Italy

Authors and Affiliations

  1. Scuola Normale Superiore and INFN-Sezione di Pisa, 56100, Pisa, Italy

    Sergio Caracciolo

  2. Department of Physics, Princeton University, 08544, Princeton, New Jersey

    Andrea Pelissetto

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

    AJan D. Sokal

Authors
  1. Sergio Caracciolo
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  2. Andrea Pelissetto
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  3. AJan D. Sokal
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Caracciolo, S., Pelissetto, A. & Sokal, A.D. Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints. J Stat Phys 67, 65–111 (1992). https://doi.org/10.1007/BF01049027

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  • DOI: https://doi.org/10.1007/BF01049027

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