Enumeration of directed site animals on the decorated square lattices

Agha Afsar Ali

Physica A: Statistical Mechanics and its Applications, 1994, vol. 202, issue 3, 520-528

Abstract: We study the problem of directed site lattice animals on decorated square lattice using its equivalence to the probabilistic cellular automata. By mapping this problem to a special case of a triangular Ising model in external field, we prove that the generating function of number of animals satisfy a quadratic equation, as was conjectured by Andrew Conway. The coupling constants of the latter satisfy the disorder condition, and it reduces to a problem already solved by Jaekel and Maillard. We also establish a connection of this problem with the problem of anisotropic directed bond percolation on a square lattice.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:202:y:1994:i:3:p:520-528

DOI: 10.1016/0378-4371(94)90476-6

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