Journal of Statistical Physics

, Volume 140, Issue 2, pp 349–392 | Cite as

Efficient Implementation of the Pivot Algorithm for Self-avoiding Walks

  • Nathan Clisby


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.


Self-avoiding walk Polymer Monte Carlo Pivot algorithm 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and StatisticsThe University of MelbourneVictoriaAustralia

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