Series expansion study of the pair connectedness in bond percolation models

Abstract

The pair connectedness C(r,p) in a percolation model is the probability that a lattice site at position r belongs to a finite cluster containing the origin when neighbouring sites are connected with probability p. Low-density power series expansions have been used to show that the spherical moments of C(r,p) are consistent with a scaling form. Assuming scaling theory to be valid, the results may be used to estimate the exponent describing the vanishing of percolation probability.