Journal of Statistical Physics

, Volume 106, Issue 3–4, pp 407–429 | Cite as

A Faster Implementation of the Pivot Algorithm for Self-Avoiding Walks

  • Tom Kennedy


The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the self-avoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is accepted; otherwise, it is rejected. Past implementations of the algorithm required a time O(N) per accepted pivot, where N is the number of steps in the walk. We show how to implement the algorithm so that the time required per accepted pivot is O(N q ) with q<1. We estimate that q is less than 0.57 in two dimensions, and less than 0.85 in three dimensions. Corrections to the O(N q ) make an accurate estimate of q impossible. They also imply that the asymptotic behavior of O(N q ) cannot be seen for walk lengths which can be simulated. In simulations the effective q is around 0.7 in two dimensions and 0.9 in three dimensions. Comparisons with simulations that use the standard implementation of the pivot algorithm using a hash table indicate that our implementation is faster by as much as a factor of 80 in two dimensions and as much as a factor of 7 in three dimensions. Our method does not require the use of a hash table and should also be applicable to the pivot algorithm for off-lattice models.

self-avoiding walk pivot algorithm polymer 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Tom Kennedy
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucson

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