Universal finite-size scaling functions for percolation on three-dimensional lattices

Using a histogram Monte Carlo simulation method ~HMCSM!, Hu, Lin, and Chen found that bond and site percolation models on planar lattices have universal finite-size scaling functions for the existence probability Ep , the percolation probability P , and the probability Wn for the appearance of n percolating clusters in these models. In this paper we extend above study to percolation on three-dimensional lattices with various linear dimensions L . Using the HMCSM, we calculate the existence probability Ep and the percolation probability P for site and bond percolation on a simple-cubic ~sc! lattice, and site percolation on body-centered-cubic and face-centered-cubic lattices; each lattice has the same linear dimension in three dimensions. Using the data of Ep and P in a percolation renormalization group method, we find that the critical exponents obtained are quite consistent with the universality of critical exponents. Using a small number of nonuniversal metric factors, we find that Ep and P have universal finite-size scaling functions. This implies that the critical Ep is a universal quantity, which is 0.26560.005 for free boundary conditions and 0.92460.005 for periodic boundary conditions. We also find that Wn for site and bond percolation on sc lattices have universal finite-size scaling functions. @S1063-651X~98!09008-4#