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Efficient Implementation of the Pivot Algorithm for Self-avoiding Walks

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Abstract

The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures and algorithms used, and provide a heuristic argument that the mean time per attempted pivot for N-step self-avoiding walks is O(1) for the square and simple cubic lattices. Numerical experiments conducted for self-avoiding walks with up to 268 million steps are consistent with o(log N) behavior for the square lattice and O(log N) behavior for the simple cubic lattice. Our method can be adapted to other models of polymers with short-range interactions, on the lattice or in the continuum, and hence promises to be widely useful.

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  1. ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria, 3010, Australia

    Nathan Clisby

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  1. Nathan Clisby
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Correspondence to Nathan Clisby.

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Clisby, N. Efficient Implementation of the Pivot Algorithm for Self-avoiding Walks. J Stat Phys 140, 349–392 (2010). https://doi.org/10.1007/s10955-010-9994-8

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  • DOI: https://doi.org/10.1007/s10955-010-9994-8

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