Site percolation thresholds for Archimedean lattices

Precise thresholds for site percolation on eight Archimedean lattices are determined by the hull-walk gradient-percolation simulation method, with the results p_c=0.697043, honeycomb or (6³), 0.807 904 (3,12²), 0.747 806 (4,6,12), 0.729 724 (4,8²), 0.579 498 (3⁴,6), 0.621 819 (3,4,6,4), 0.550 213 (3³,4²), and 0.550 806 (3²,4,3,4), with errors of about ±3×10^-6. [The remaining Archimedean lattices are the square (4⁴), triangular (3⁶), and Kagomé (3,6,3,6), for which p_c is already known exactly or to a high degree of accuracy.] The numerical result for the (3,12²) lattice is consistent with the exact value [1-2sin(π/18)]^1/2. The values of p_c for all 11 Archimedean lattices, as well as a number of nonuniform lattices, are found to be well correlated by a nearly linear function of a generalized Scher-Zallen filling factor. This correlation is much more accurate than recently proposed correlations based solely upon coordination number.