Critical Percolation Probabilities by Series Methods

Abstract

Series estimates of the critical percolation probabilities for the "bond problem" and the "site problem" are presented for two- and three-dimensional lattices. Good agreement with the Monte Carlo estimates of Frisch et al. and of Dean is obtained. The series method gives information on the critical behavior of the mean cluster size and it is found that there is a much sharper growth of large clusters in two dimensions than in three dimensions as the critical concentration is approached from below.