Large lattice random site percolation

We simulate the two dimensional (2d), simple square and three-dimensional ( 3d), simple cubic random site percolation systems for L = 2 000 000 (2d) an d L = 10001 (3d) at the percolation thresholds for these systems. We report excellent agreement with the Fisher exponent, tau, in 2d, with the propose d exact value 187/91 and good agreement with other good high quality simula tion results in 3d of 2.186. We have also computed how the first, second, t hird,..., largest clusters scale with L at the percolation threshold. These clusters all scale with the same fractal dimensionality as the largest clu ster. (C) 1999 Elsevier Science B.V. All rights reserved.