We study bond percolation on the simple cubic 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 additional nearest neighbors, we find $p_c(z-1)=1+1.224z^{-1/2}$.

中文翻译：

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在具有扩展邻域的简单立方晶格上的键渗透。

我们通过蒙特卡洛模拟研究了具有第一，第二，第三和第四最近邻的各种组合的简单立方晶格上的键渗流。使用单簇增长算法，我们可以找到键值阈值的精确值。讨论了渗流阈值与晶格性质之间的相关性，我们的结果表明，这些和其他三维晶格的渗流阈值随配位数而单调降低$ž$ 根据幂定律非常准确 $p_C〜{ž}^{-\mathrm{一种}}$ 有指数 $\mathrm{一种}=1.111$。但是，对于大$ž$，阈值必须接近Bethe晶格结果 $p_C=\mathrm{1个}/（ž-\mathrm{1个}）$。拟合我们的数据和其他最近邻的数据，我们发现$p_C（ž-\mathrm{1个}）=\mathrm{1个}+1.224{ž}^{-\mathrm{1个}/2}$。