DEPENDENCE OF PERCOLATION THRESHOLDS ON LATTICE CONNECTIVITY

We investigate site percolation on lattices with directed bonds. Numer ical simulations in which the lattice coordination number of the perco lation lattices is systematically varied show that the inverse of the percolation threshold depends approximately linearly on the lattice co ordination number. We show that this linear relationship is due to a s imilarity of percolation clusters in lattices for different coordinati on numbers, We compare this relationship to results obtained by Flory [Principles of Polymer Chemistry (Cornell University Press, Ithaca, Ne w York, 1953), Chap. IX] in the study of gelation processes and discus s its general applicability for related percolation models.