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A Monte Carlo algorithm for lattice ribbons

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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.

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Authors and Affiliations

  1. Department of Theoretical Physics, OX1 3NP, Oxford, England

    E. Orlandini

  2. Department of Mathematics and Statistics, York University, M3J 1P3, North York, Ontario, Canada

    E. J. Janse van Rensburg

  3. Department of Chemistry, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    S. G. Whittington

Authors
  1. E. Orlandini
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  2. E. J. Janse van Rensburg
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  3. S. G. Whittington
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Orlandini, E., Janse van Rensburg, E.J. & Whittington, S.G. A Monte Carlo algorithm for lattice ribbons. J Stat Phys 82, 1159–1198 (1996). https://doi.org/10.1007/BF02179807

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  • DOI: https://doi.org/10.1007/BF02179807

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