Improved lower bounds on the connective constants for two-dimensional self-avoiding walks

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Abstract

We calculate improved lower bounds for the connective constants for self-avoiding walks on the square, hexagonal, triangular, (4.82) and (3.122) lattices. The bound is found by Kesten's method of irreducible bridges. This involves using transfer-matrix techniques to exactly enumerate the number of bridges of a given span to very many steps. Upper bounds are obtained from recent exact enumeration data for the number of self-avoiding walks and compared to current best available upper bounds from other methods.

Original languageEnglish
Pages (from-to)11521-11529
Number of pages9
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number48
DOIs
Publication statusPublished - 17 Nov 2004
Externally publishedYes

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