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

Abstract

We calculate improved lower bounds for the connective constants for self-avoiding walks on the square, hexagonal, triangular, $(4.8^2)$, and $(3.12^2)$ 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.