Random Site Percolation in Three Dimensions

We simulate sytems up to 10 001 × 10 001 × 10 001 in three dimensions at the percolation threshold pc of 0.31160. We find that the fractal dimension is ≃2.53±0.02, the cluster size distribution exponent, τ, is 2.186±0.002 and an exponent of 0.85 describing how the mass of the clusters scale with rank. Corrections-to-scaling exponents of ≃-0.7 are observed for ns and for the mass of the largest cluster. We also check the percolation threshold and report good agreement with recent values.