Size distribution of percolating clusters on cubic lattices

We present Monte Carlo simulations of site percolation on cubic lattices with size L. The cut-off function of the size distribution at the characteristic size s* can be described by a Gaussian for site occupations (p) lower than the critical value for percolation (p(c)) while for p > p(c) it is better described by a stretched exponential. Finite lattice size effects depend on both epsilon = (p(c) - p)/p(c) and L and cannot be eliminated by normalization with the distribution at epsilon = 0. We give a general expression of the cut-off function valid for any epsilon sufficiently small and L sufficiently large. Using this general expression, we calculate the finite lattice size effects on the weight average (s(w)) and z-average (s(z)) sizes which are in good agreement with values directly obtained from the simulations.