Abstract
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.
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Barkema, G.T., Flesia, S. Two-dimensional oriented self-avoiding walks with parallel contacts. J Stat Phys 85, 363–381 (1996). https://doi.org/10.1007/BF02174210
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DOI: https://doi.org/10.1007/BF02174210