Site percolation thresholds for Archimedean lattices

Precise thresholds for site percolation on eight Archimedean lattices ate d etermined by the hull-walk gradient-percolation simulation method, with the results p(c) = 0.697043, honeycomb or (6(3)), 0.807904 (3,12(2)), 0.747806 (4,6,12), 0.729724 (4,8(2)), 0.579498 (3(4),6), 0.621819 (3,4,6,4), 0.5502 13 (3(3),4(2)), and 0.550806 (3(2),4,3,4), with errors of about +/- 3 x 10( -6). [The remaining Archimedean lattices are the square (4(4)), triangular (3(6)), and Kagome (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 i s consistent with the exact value [1-2 sin(pi/18)](1/2). The values of p(c) for all 11 Archimedean lattices, as well as a number of nonuniform lattice s, are found to be well correlated by a nearly linear function of a general ized Scher-Zallen filling factor. This correlation is much more accurate th an recently proposed correlations based solely upon coordination number. [S 1063-651X(99)11207-8].