Abstract. We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kesten's method of irreducible bridges and by determining generating functions for bridges on one-dimensional lattices. The upper bound is obtained as the largest eigenvalue of a certain transfer matrix. Using a relation between the hexagonal and the (3.12²) lattices, we also give bounds for the connective constant of the latter lattice.

PACS number: 05.50.+q

Mathematics Subject Classification: 05A15, 05C40

Print publication: Issue 3 (23 January 2004)
Received 8 July 2003, in final form 26 September 2003
Published 7 January 2004