Universal formulas for percolation thresholds.

A power law is postulated for both site and bond percolation thresholds. The formula writes pc = p0[(d − 1)(q − 1)]d , 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 first two classes b = 0 for site dilution while b = a for bond dilution. The last one associated to 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. Permanent adress: Groupe de Physique des Solides, T23, Universités Paris 7 et 6, 2 Place Jussieu, 75751 Paris Cedex 05 Laboratoire associé au CNRS (URA n 800) et à l’Université P. et M. Curie Paris 6