Two-dimensional oriented self-avoiding walks with parallel contacts |
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Authors: | G T Barkema S Flesia |
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Institution: | (1) Institute for Advanced Study, 08540 Princeton, New Jersey;(2) Theoretical Physics, University of Oxford, OX1 3NP Oxford, UK;(3) Department of Mathematics, Imperial College, SW7 2BZ London, UK |
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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 at
s
=log(), where -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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Keywords: | Self-avoiding walks oriented walks collapse spiral walks Monte Carlo exact enumeration |
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