Percolation threshold of a class of correlated lattices

Investigations have been made of the percolation threshold of correlated site percolation lattices based on the convolution of a smoothing function with random white noise as suggested by Crossley, Schwartz, and Banavar. The dependence of percolation threshold on correlation length has been studied for several smoothing functions, lattice types, and lattice sizes. All results can be fit by a Gaussian function of the correlation length w,p(c)=p(c)(infinity)+(p(c)(0)-pc(infinity))e(-alpha w2). For two-dimensional, matching lattices the thresholds satisfy the Sykes-Essam relation p(c)(L)+p(c)(L*)=1.