Suding P N, Ziff R M
Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jul;60(1):275-83. doi: 10.1103/physreve.60.275.
Precise thresholds for site percolation on eight Archimedean lattices are determined by the hull-walk gradient-percolation simulation method, with the results p(c)=0.697 043, 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 0.550 806 (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 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 (3,12(2)) lattice is consistent with the exact value 1-2 sin(pi/18). 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.
通过包络行走梯度渗流模拟方法确定了八个阿基米德晶格上的位点渗流精确阈值，结果为：p(c)=0.697 043，蜂窝晶格或(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))；以及0.550 806 (3(2),4,3,4)，误差约为±3×10⁻⁶。其余阿基米德晶格为正方形(4(4))、三角形(3(6))和 Kagomé 晶格(3,6,3,6)，其 p(c) 已精确得知或具有高精度。晶格的数值结果与精确值[1 - 2sin(π/18)]^(1/2)一致。发现所有11个阿基米德晶格以及一些非均匀晶格的 p(c) 值与广义舍尔 - 扎伦填充因子的近似线性函数具有良好的相关性。这种相关性比最近仅基于配位数提出的相关性要准确得多。
