SITE PERCOLATION THRESHOLDS IN ALL DIMENSIONS

Site percolation thresholds are reproduced in all dimensions for all l attices using a linear combination of two analytic terms. One is the w ell known Cayley tree percolation threshold which is believed to be ex act at infinite dimension. The other one is obtained from a new approa ch 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 = infinity. Our results agree with exact numerical estimates f or any lattice in any dimension within few percent.