Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
Zhipeng Xun,
DaPeng Hao,
Robert M. Ziff
Abstract:Extended-range percolation on various regular lattices, including all eleven Archimedean lattices in two dimensions, and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number z and site thresholds pc for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting z versus 1/pc and z versus −1/ ln(1 − pc), using the data of d'Iribarne et al. [J. Phys. A 32:2611[J.… Show more
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