Series study of random percolation in three dimensions

New high-density series data for the mean number, percolation probability and 'susceptibility' of finite clusters are presented for bond and site percolation on four standard three-dimensional lattices.Our Pad6 approximant analysis of both high-and low-density series makes particular use of the rather precise unbiased estimates of the percolation threshold, pc, obtained recently by Heermann and Stauffer for the simple cubic lattice.For this lattice we obtain the biased estimate y = 1.73 50.03 for the site problem and a similar estimate but with larger uncertainties for the bond problem.Such a value is significantly larger than earlier series estimates.Assuming y to be universal, we obtain precise, although biased, estimates of pc for both bond and site percolation on all four lattices.Using the bond estimates of p c we find an overall biased estimate of /3 = 0.454 0.008 for bond percolation on all three-dimensional lattices.(The corresponding site problem requires further study.)Scaling estimates of other critical exponents are U = -0 .6 4 i 0 .0 5 , 8 = 4 .8 1 * 0 . 1 4 , A = 2 . 1 8 i 0 .0 4 , v=0.88*0.02andr)=0.03+.0.03.~~( B c c ) , 36(sc), 2 5 ( ~) and for the site problem N = ~~( F c c ) , ~~( B c c ) , 33(sc), ~O ( D ) .Further details and additional data will be published in due course.