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

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

2004-09-15

arxiv.org/abs/cond-mat/0409381v2

J. Phys. A 37, 11521-11529 (2004)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/0305-4470/37/48/001

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.

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