Two-dimensional oriented self-avoiding walks with parallel contacts

Details Two-dimensional oriented self-avoiding walks with parallel contacts Two-dimensional oriented self-avoiding walks with parallel contacts

1996-03-29

arxiv.org/abs/cond-mat/9603193v1

Physics

Condensed Matter

12 pages, revtex, 10 separate PostScript figures

Scientific paper

10.1007/BF02174210

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 a first-order phase transition from a free phase to a tight-spiral phase at $\beta_c=\log(\mu)$, where $\mu =2.638$ 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.

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