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基于高效的单团簇生长算法, 采用蒙特卡罗方法模拟了考虑最近邻、次近邻, 直至第五近邻格点的二维正方格子的键渗流. 计算得到了二十余种格点模型高精度的键渗流阈值, 并深入探讨了渗流阈值
$p_{\rm c}$ 与格点结构之间的关联. 通过引入参数$\xi = \displaystyle\sum\nolimits_{i} z_{i} r_{i}^{2} / i$ (其中$z_{i}$ 和$r_{i}$ 分别为第 i近邻格点的配位数及到中心格点的距离)来消除“简并”, 研究发现$p_{\rm c}$ 随 ξ的变化较好地满足幂律关系$p_{\rm c} \propto \xi^{-\gamma}$ , 数值拟合得$\gamma \approx 1$ .Based on an effective single cluster growth algorithm, bond percolation on square lattice with the nearest neighbors, the next nearest neighbors, up to the 5th nearest neighbors are investigated by Monte Carlo simulations. The bond percolation thresholds for more than 20 lattices are deduced, and the correlations between percolation threshold$p_{\rm c}$ and lattice structures are discussed in depth. By introducing the index$\xi = \displaystyle\sum\nolimits_{i} z_{i} r_{i}^{2} / i$ to remove the degeneracy, it is found that the thresholds follow a power law$p_{\rm c} \propto \xi^{-\gamma}$ , with$\gamma \approx 1$ , where$z_{i}$ is the ith neighborhood coordination number, and$r_{i}$ is the distance between sites in the i-th coordination zone and the central site.[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] -
格点模型 总配
位数z标量
参数ξ键渗流阈值 $p_{\rm c}$ SQ-1, 2,
SQ-2, 58 8 0.2503683(7) $\text{SQ-}1, 3$ 8 9.33 0.2214989(9) $\text{SQ-}1, 5$ 8 10.4 0.1972557(13) $\text{SQ-}4$ 8 10 0.1937380(10) SQ-1, 2, 3,
SQ-2, 3, 512 13.33 0.1522201(9) $\text{SQ-}1, 2, 5$ 12 14.4 0.1380527(7) $\text{SQ-}1, 4$ 12 14 0.1362105(5) $\text{SQ-}2, 4$ 12 14 0.1345500(10) $\text{SQ-}1, 3, 5$ 12 15.73 0.1342972(8) $\text{SQ-}3, 4$ 12 15.33 0.1309686(14) $\text{SQ-}4, 5$ 12 16.4 0.1247135(15) $\text{SQ-}1, 2, 4$ 16 18 0.1059928(8) $\text{SQ-}1, 2, 3, 5$ 16 19.73 0.1032173(7) $\text{SQ-}1, 3, 4$ 16 19.33 0.1027026(6) $\text{SQ-}2, 3, 4$ 16 19.33 0.1011488(8) $\text{SQ-}1, 4, 5$ 16 20.4 0.0978026(14) $\text{SQ-}2, 4, 5$ 16 20.4 0.0967349(11) $\text{SQ-}3, 4, 5$ 16 21.73 0.0954613(7) $\text{SQ-}1, 2, 3, 4$ 20 23.33 0.0841507(7) $\text{SQ-}1, 2, 4, 5$ 20 24.4 0.0804649(9) $\text{SQ-}1, 3, 4, 5$ 20 25.73 0.0790839(9) $\text{SQ-}2, 3, 4, 5$ 20 25.73 0.0780764(6) $\text{SQ-}1, 2, 3, 4, 5$ 24 29.73 0.0671855(5) 
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第i近邻 距中心格点
距离的平方 $r_{i}^{2}$第i近邻
格点数 $z_{i}$总配位数z 1 1 4 4 2 2 4 8 3 4 4 12 4 5 8 20 5 8 4 24 下载:
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