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 n_s of percolation clusters with s occupied sites each is calculated by up to 19 runs on a 4000*4000 triangular lattice near p_c. The data support the two-exponent scaling assumption n_s varies as s^{- tau} f(z'), where z'=(p/p_c-1)s^sigma .