Universal formulas for percolation thresholds

A power law is postulated for both site and bond percolation thresholds. The formula is pc=p₀[(d-1)(q-1)]^-a{d}ᵇ$, where d is the space dimension and q the coordination number. All thresholds up to d{→}{∞} are found to belong to only three universality classes. For two classes b=0 for site dilution while b=a for bond dilution. The remaining class associated with high dimensions is characterized by b=2a-1 for both sites and bonds. Classes are defined by a set of value for {p₀;a}. Deviations from available numerical estimates at d{≤}7 are within ±{}0.008 and ±{}0.0004 for high dimensional hypercubic expansions at d{≥}8. The formula is found to be also valid for Ising critical temperatures. {} 1996 The American Physical Society.