Monte Carlo experiments on cluster size distribution in percolation

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 .