Universal scaling functions for bond percolation on planar-random and square-lattices with multiple percolating clusters - art. no. 016127

Percolation models with multiple percolating clusters have attracted much a ttention in recent years. Here we use Monte Carlo simulations to study bond percolation on L-1 x L-2 planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertica l and horizontal directions, respectively, and with various aspect ratios L -1/L-2. We calculate the probability for the appearance of n percolating cl usters, W-n; the percolating probabilities P; the average fraction of latti ce bonds (sites) in the percolating clusters, [c(b)](n) ([c(s)](n)), and th e probability distribution function for the fraction c of lattice bonds (si res), in percolating clusters of subgraphs with n percolating clusters, f(n )(c(b)) [f(n)(C-5)]. Using a small number of nonuniversal metric factors, w e find that W-n, P, [c(b)](n) ([c(s)](n)), and f(n)(c(b)) [f(n)(c(s))] for random lattices, duals of random lattices, and square lattices have the sam e universal finite-size scaling functions. We also find that nonuniversal m etric factors are independent of boundary conditions and aspect ratios.