Upper and Lower Bounds for the Connective Constants of Self-avoiding Walks on the Archimedean and Laves Lattices


Sven Erick Alm

Uppsala University

In: J. Phys. A: Math. Gen. 38 (2005), 2055-2080



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.

2010-03-04, Sven Erick Alm, sea@math.uu.se