Upper and Lower Bounds for the Connective Constants of Self-avoiding Walks on the Archimedean and Laves Lattices
by
Sven Erick Alm
Uppsala University
In: J. Phys. A: Math. Gen. 38 (2005), 2055-2080
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Abstract
We give improved upper and lower bounds for the connective constants
of self-avoiding walks on a class of lattices, including the
Archimedean and Laves lattices. The lower bounds are obtained by
using Kesten's method of irreducible bridges, with an appropriate
generalisation for weakly regular lattices.
The upper bounds are obtained as the largest eigenvalue of a certain
transfer matrix.
The obtained bounds show that, in the studied class of lattices, the
connective constant is increasing in the average degree of the
lattice. We also discuss an alternative measure of average degree.