论文标题
粘合渗透在简单的立方格子上，延伸社区
Bond percolation on simple cubic lattices with extended neighborhoods
论文作者
论文摘要
我们通过Monte Carlo Simulation研究了简单立方（SC）晶格上的键渗透，其第一，第二，第三和第四个邻居的键合。使用单群集生长算法，我们找到键阈值的精确值。讨论了渗透阈值和晶格属性之间的相关性，我们的结果表明，根据Power Law $ p _ {c} \ sim z^{ - s z^{ - a} $，p _ $ p _ = 1.111 $ a = 1.11111，这些和其他三维晶格的渗透阈值单次降低单调降低。但是，对于大$ z $，阈值必须接近伯特晶格结果$ p_c = 1/（z-1）$。将我们的数据和数据与其他最近的邻居拟合，我们发现$ P_C（Z-1）= 1+1.224 Z^{ - 1/2} $。
We study bond percolation on the simple cubic (SC) lattice with various combinations of first, second, third, and fourth nearest-neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the bond thresholds. Correlations between percolation thresholds and lattice properties are discussed, and our results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number $z$ quite accurately according to a power law $p_{c} \sim z^{-a}$, with exponent $a = 1.111$. However, for large $z$, the threshold must approach the Bethe lattice result $p_c = 1/(z-1)$. Fitting our data and data for lattices with additional nearest neighbors, we find $p_c(z-1)=1+1.224 z^{-1/2}$.
