Percolation thresholds and universal formulas

Abstract

A calculation of percolation thresholds of 11 two-dimensional and 18 three-dimensional lattices is presented. Among the three-dimensional ones are a random lattice and its dual, plus a number of aniso- tropic regular lattices. The results are used to test universal formulas that relate the percolation thresholds of lattices to their dimension and coordination number. The evidence suggests that dimension and coordination number are not sufficient to predict percolation thresholds.