摘要: Precise thresholds for site percolation on eight Archimedean lattices are determined by the hull-walk gradient-percolation simulation method, with results p(c)=0.697 043, honeycomb or (6(3)), 0.807 904 (3,12(2)), 0.747 806 (4,6,12), 0.729 724 (4,8(2)), 0.579 498 (3(4),6), 0.621 819 (3,4,6,4), 0.550 213 (3(3),4(2)), and (3(2),4,3,4), errors of about +/- 3 x 10(-6). [The remaining square (4(4)), triangular (3(6)), Kagome (3,6,3,6), which p(c) is already known exactly to a high degree accuracy.] The numerical result (3,12(2)) lattice consistent exact value [1-2 sin(pi/18)](1/2). values all 11 lattices, as well number nonuniform found be correlated nearly linear function generalized Scher-Zallen filling factor. This correlation much more accurate than recently proposed correlations based solely upon coordination number.
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