Journal of Statistical Physics

, Volume 85, Issue 3–4, pp 363–381 | Cite as

Two-dimensional oriented self-avoiding walks with parallel contacts

  • G. T. Barkema
  • S. Flesia


Oriented self-avoiding walks (OSAWs) on a square lattice are studied, with binding energies between steps that are oriented parallel across a face of the lattice. By means of exact enumeration and Monte Carlo simulation, we reconstruct the shape of the partition function and show that this system features of first-order phase transition from a free phase to a tight-spiral phase atΒ s =log(μ), where μ-2.638 is the growth constant for SAWs. With Monte Carlo simulations we show that parallel contacts happen predominantly between a step close to the end of the OSAW and another step nearby; this appears to cause the expected number of parallel contacts to saturate at large lengths of the OSAW.

Key Words

Self-avoiding walks oriented walks collapse spiral walks Monte Carlo exact enumeration 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • G. T. Barkema
    • 1
  • S. Flesia
    • 2
    • 3
  1. 1.Institute for Advanced StudyPrinceton
  2. 2.Theoretical PhysicsUniversity of OxfordOxfordUK
  3. 3.Department of MathematicsImperial CollegeLondonUK

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