Exact results for average cluster numbers in bond percolation on lattice strips.
We present exact calculations of the average number of connected clusters per site, <k>, as a function of bond occupation probability p, for the bond percolation problem on infinite-length strips of finite width Ly, of the square, triangular, honeycomb, and kagomé lattices Lambda with various boundary conditions. These are used to study the approach of <k>, for a given p and Lambda, to its value on the two-dimensional lattice as the strip width increases. We investigate 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 .
Chang
Shu-Chiuan
SC
Physics Division, National Center for Theoretical Sciences at Taipei, National Taiwan University, Taipei 10617, Taiwan. scchang@mail.ncku.edu.tw
Shrock
Robert
R