三角格点上含有五配位带的邻域的逾渗阈值
Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone
摘要：
我们确定阈值$p_c$随机网站渗流的三角形晶格上的所有可用的邻居包含网站从第一到第五协调区，包括其复杂的组合。有31个不同的街区。的渗滤阈值$p_c$的配位数$z$的值的依赖性进行测试对各种理论预测。新提出的单个标量索引$ξ=\sum_i z_ir_i^2/i$（取决于协调区编号$i$、邻域协调编号$z$和从中心位点到第$i$协调区中的位点的平方距离$r^2$）允许区分各种邻域并将$p_c$与$ξ$相关。阈值大致遵循$p_c\proptoξ^{-γ}$与$γ\approx 0.710(19)$的幂律。
英文摘要：
We determine thresholds $p_c$ for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their complex combinations. There are 31 distinct neighbourhoods. The dependence of the value of the percolation thresholds $p_c$ on the coordination number $z$ are tested against various theoretical predictions. The newly proposed single scalar index $ξ=\sum_i z_ir_i^2/i$ (depending on the coordination zone number $i$, the neighbourhood coordination number $z$ and the square-distance $r^2$ to sites in $i$-th coordination zone from the central site) allows to differentiate among various neighbourhoods and relate $p_c$ to $ξ$. The thresholds roughly follow a power law $p_c\proptoξ^{-γ}$ with $γ\approx 0.710(19)$.
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