Bond Percolation Critical Probability Bounds for Three Archimedean Lattices

Abstract

Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: .7385 < pc((3, 12 22) bond) < pc ((4, 6, 12) bond) < pc((4, 82) bond) < .7201. Consequently, the bond percolation critical probability of the (3, 12 2) lattice is strictly larger than those of the other ten Archimedean lattices. Thus, the (3, 122) bond percolation critical probability is possibly the largest of any vertex-transitive graph with bond percolation critical probability that is strictly less than one. © 2002 Wiley Periodicals, Inc.