Universality of critical existence probability for percolation on three-dimensional lattices

Abstract

Using a histogram Monte Carlo simulation method, we calculate the existence probability for bond percolation on simple cubic (sc) and body-centred cubic (bcc) lattices, and site percolation on sc lattices with free boundary conditions. The spanning rule considered by Reynolds, Stanley, and Klein is used to define percolating clusters. We find that for such systems has very good finite-size scaling behaviour and the value of at the critical point is universal and is about .