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.