Exact results for average cluster numbers in bond percolation on lattice strips

Th exact calculations of the average cluster per site <k> for the bond percolation problem on infinite-length, finite-width strips of the square, triangular, honeycomb, and kagomé lattices, with both free and periodic transverse boundary conditions were presented. The singularities of <k> in the complex p plane and their influence on the radii of convergence of the Taylor series expansions of <k> about p=0 and p=1 were investigated. The approach of <k>, for a given p and λ, to its value on the two-dimensional lattice as the strip width increases, was also studied. The free energy for the Potts model on the 2_F strip of the kagomé lattice was also given.