UNIVERSALITY OF CRITICAL EXISTENCE PROBABILITY FOR PERCOLATION ON 3-DIMENSIONAL LATTICES

Using a histogram Monte Carlo simulation method, we calculate the exis tence probability E-p for bond percolation on simple cubic (sc) and bo dy-centred cubic (bcc) lattices, and site percolation on sc lattices w ith free boundary conditions. The R-1 spanning rule considered by Reyn olds, Stanley, and Klein is used to define percolating clusters. We fi nd that E-p for such systems has very good finite-size scaling behavio ur and the value of E-p at the critical point is universal and is abou t 0.265 +/- 0.005.