Monte Carlo experiments on cluster size distribution in percolation

Abstract

Cluster statistics in two- and three-dimensional site percolation problems are derived here by Monte Carlo methods. The average number ns of percolation clusters with s occupied sites each is calculated by up to 19 runs on a 4000*4000 triangular lattice near pc. The data support the two-exponent scaling assumption ns varies as s- tau f(z'), where z'=(p/pc-1)ssigma .