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 E-p, the percolation probability P, and the probability W-n 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 E-p 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 E-p 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 E-p and P have universal finite-size scaling functions. This implies that the critical E-p is a universal quantity, which is 0.265 +/- 0.005 for free boundary conditions and 0.924 +/- 0.005 for periodic boundary conditions. We also find that W-n for site and bond percolation on sc lattices have universal finite-size scaling functions.