Percolation thresholds and Fisher exponents in hypercubic lattices.
We use invasion percolation to compute highly accurate numerical values for bond and site percolation thresholds p_{c} on the hypercubic lattice Z^{d} for d=4,...,13. We also compute the Fisher exponent τ governing the cluster size distribution at criticality. Our results support the claim that the mean-field value τ=5/2 holds for d≥6, with logarithmic corrections to power-law scaling at d=6.