Percolation Thresholds and Fisher Exponents in Hypercubic Lattices
arXiv:1806.08067 · doi:10.1103/PhysRevE.98.022120
Abstract
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 tau governing the cluster size distribution at criticality. Our results support the claim that the mean-field value tau = 5/2 holds for d >= 6, with logarithmic corrections to power-law scaling at d=6.