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.

PACS numbers: 05.50.+q, 05.10.−a, 02.10.Ox

Print publication: Issue 48 (3 December 2004)
Received 10 September 2004, in final form 8 October 2004
Published 17 November 2004