Journal of Statistical Physics

, Volume 50, Issue 1–2, pp 109–186 | Cite as

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk

  • Neal Madras
  • Alan D. Sokal


The pivot algorithm is a dynamic Monte Carlo algorithm, first invented by Lal, which generates self-avoiding walks (SAWs) in a canonical (fixed-N) ensemble with free endpoints (hereN is the number of steps in the walk). We find that the pivot algorithm is extraordinarily efficient: one “effectively independent” sample can be produced in a computer time of orderN. This paper is a comprehensive study of the pivot algorithm, including: a heuristic and numerical analysis of the acceptance fraction and autocorrelation time; an exact analysis of the pivot algorithm for ordinary random walk; a discussion of data structures and computational complexity; a rigorous proof of ergodicity; and numerical results on self-avoiding walks in two and three dimensions. Our estimates for critical exponents areυ=0.7496±0.0007 ind=2 andυ= 0.592±0.003 ind=3 (95% confidence limits), based on SAWs of lengths 200⩽N⩽10000 and 200⩽N⩽ 3000, respectively.

Key words

Self-avoiding walk polymer Monte Carlo pivot algorithm critical exponent 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Neal Madras
    • 1
  • Alan D. Sokal
    • 2
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Department of PhysicsNew York UniversityNew York

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