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Journal of Statistical Physics

, Volume 82, Issue 3–4, pp 1159–1198 | Cite as

A Monte Carlo algorithm for lattice ribbons

  • E. Orlandini
  • E. J. Janse van Rensburg
  • S. G. Whittington
Articles

Abstract

A lattice ribbon is a connected sequence of plaquettes subject to certain selfavoidance conditions. The ribbon can be closed to form an object which is topologically either a cylinder or a Möbius band, depending on whether its surface is orientable or nonorientable. We describe a grand canonical Monte Carlo algorithm for generating a sample of these ribbons, prove that the associated Markov chain is ergodic, and present and discuss numerical results about the dimensions and entanglement complexity of the ribbons.

Key Words

Ribbon lattice models Monte Carlo algorithm knotting and linking entanglements 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. Orlandini
    • 1
  • E. J. Janse van Rensburg
    • 2
  • S. G. Whittington
    • 3
  1. 1.Department of Theoretical PhysicsOxfordEngland
  2. 2.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada
  3. 3.Department of ChemistryUniversity of TorontoTorontoCanada

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