On the asymptotic number of lattice animals in bond and site percolation

Abstract

A recently proposed asymptotic form, due to Domb (1976), for the total number of bond and site animals of size n, has been investigated numerically. It is found to fit the available data better than simpler forms previously assumed. The critical parameters entering into the asymptotic form are estimated for a number of two- and three-dimensional lattices, and conclusions are drawn about their lattice and dimensional dependence. In particular, the cluster growth parameter lambda is estimated with a higher degree of precision than that previously attained.