Journal of Statistical Physics

, Volume 67, Issue 1–2, pp 65–111 | Cite as

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

  • Sergio Caracciolo
  • Andrea Pelissetto
  • AJan D. Sokal


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 stepsNtot 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.

Key words

Self-avoiding walk polymer Monte Carlo join- and-cut algorithm pivot algorithm critical exponent 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Sergio Caracciolo
    • 1
  • Andrea Pelissetto
    • 2
  • AJan D. Sokal
    • 3
  1. 1.Scuola Normale Superiore and INFN-Sezione di PisaPisaItaly
  2. 2.Department of PhysicsPrinceton UniversityPrinceton
  3. 3.Department of PhysicsNew York UniversityNew York

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