Abstract
A transfer matrix method for treating self-avoiding walks on a lattice is developed. Single walks confined to infinitely long strips, cylinders, or tubes are considered, particularly in the limit where the length of the walk becomes infinite compared to the transverse dimensions. In this case relevant distributions are demonstrated to be asymptotically Gaussian. Explicit numerical results are given for a few of the narrower systems. Similar results for self-avoiding cycles are indicated, too. Finally, the behavior of the various distributions as a function of strip width is discussed.
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Supported by the Robert A. Welch Foundation, Houston, Texas.
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Klein, D.J. Asymptotic distributions for self-avoiding walks constrained to strips, cylinders, and tubes. J Stat Phys 23, 561–586 (1980). https://doi.org/10.1007/BF01011730
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DOI: https://doi.org/10.1007/BF01011730