Site percolation thresholds in all dimensions

Site percolation thresholds are reproduced in all dimensions for all lattices using a linear combination of two analytic terms. One is the well known Cayley tree percolation threshold which is believed to be exact at infinite dimension. The other one is obtained from a new approach to two-dimensional site dilution using a ferromagnetic Ising system. These two formulas are then combined with weighting factors a and 1 − a respectively, where a is a fitting parameter which depends only on space dimension. It is equal to 0.047 at d = 2, to 0.924 at d = 6 and 1 at d = ∞. Our results agree with exact numerical estimates for any lattice in any dimension within few percent.