Bounds for the connective constant of the hexagonal lattice
2004 (English)In: J.\ Phys. A: Math. Gen., Vol. 37, 549- p.Article in journal (Refereed) Published
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 $(3.12^2)$ lattices, we also give bounds for the connective constant of the latter lattice.
Place, publisher, year, edition, pages
2004. Vol. 37, 549- p.
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-70897DOI: doi:10.1088/0305-4470/37/3/001OAI: oai:DiVA.org:uu-70897DiVA: diva2:98808