Hamiltonian walks and polymer configurations

A. Malakis

Physica A: Statistical Mechanics and its Applications, 1976, vol. 84, issue 2, 256-284

Abstract: Kasteleyn's treatment of the hamiltonian walk problem on lattice graphs is briefly reviewed. The asymptotic behaviour of the number of hamiltonian walks on the kth covering of a closed oriented lattice graph is expressed in terms of the asymptotic behaviour of the number of oriented trees on the lattice graph. Asymptotic results on the enumeration of hamiltonian walks are presented for the covering and underlying lattices of the Manhattan oriented square lattice, and the covering lattices of certain orientations of the diamond and cubic lattices. The effect of boundary conditions is examined.

Date: 1976
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:84:y:1976:i:2:p:256-284

DOI: 10.1016/0378-4371(76)90002-9

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