论文标题
带有复杂社区的三角形晶格上的位点渗透阈值
Site percolation thresholds on triangular lattice with complex neighborhoods
论文作者
论文摘要
我们确定阈值$ p_c $用于在三角形晶格上随机渗透的阈值，用于包含最接近（NN）的邻域（NN），Next-Nearest（2NN），Next-Next-Nearest（3nn），Next-Next-Next-Next-Next-Next-nearest（4nn）（4NN）和Next-Next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-next-Nearest（Next-Next-next-next-Nearest（5nn）（ （3NN+2NN+NN，5NN+4NN+NN，5NN+4NN+3NN+2NN，5NN+4NN+4NN+3NN+2NN+NN）。我们使用Newman和Ziff的快速蒙特卡洛算法[M. E. J. Newman和R. M. Ziff，《物理评论》 E 64，016706（2001）]，用于获得最大群集大小对职业概率的依赖性。 Bastas等人将该方法与方法结合在一起。 [N. Bastas，K。Kosmidis，P。Giazitzidis和M. Maragakis，物理评论E 90，062101（2014）]，估计低统计数据的阈值。渗透阈值的估计值为$ p_c（\ text {4nn}）= 0.192410（43）$，$ p_c（\ text {3nn+2nn}）= 0.232008（38）$，$ p_c（$ p_c） $ p_c（\ text {3nn+2nn+nn}）= 0.215484（19）$，$ p_c（\ text {5nn+4nn+nn}）= 0.131792（58）$ $ p_c（\ text {5nn+4nn+3nn+2nn+nn}）= 0.115847（21）$。该方法在三角晶格上的站点渗透的标准情况下进行测试，其中$ p_c（\ text {nn}）= p_c（\ text {2nn}）= p_c（\ text {3nn}） $ p_c（\ text {nn}）= 0.500029（46）$，仅通过一千多个晶格实现。
We determine thresholds $p_c$ for random site percolation on a triangular lattice for neighbourhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN) and next-next-next-next-nearest (5NN) neighbours, and their combinations forming regular hexagons (3NN+2NN+NN, 5NN+4NN+NN, 5NN+4NN+3NN+2NN, 5NN+4NN+3NN+2NN+NN). We use a fast Monte Carlo algorithm, by Newman and Ziff [M. E. J. Newman and R. M. Ziff, Physical Review E 64, 016706 (2001)], for obtaining the dependence of the largest cluster size on occupation probability. The method is combined with a method, by Bastas et al. [N. Bastas, K. Kosmidis, P. Giazitzidis, and M. Maragakis, Physical Review E 90, 062101 (2014)], of estimating thresholds from low statistics data. The estimated values of percolation thresholds are $p_c(\text{4NN})=0.192410(43)$, $p_c(\text{3NN+2NN})=0.232008(38)$, $p_c(\text{5NN+4NN})=0.140286(5)$, $p_c(\text{3NN+2NN+NN})=0.215484(19)$, $p_c(\text{5NN+4NN+NN})=0.131792(58)$, $p_c(\text{5NN+4NN+3NN+2NN})=0.117579(41)$, $p_c(\text{5NN+4NN+3NN+2NN+NN})=0.115847(21)$. The method is tested on the standard case of site percolation on triangular lattice, where $p_c(\text{NN})=p_c(\text{2NN})=p_c(\text{3NN})=p_c(\text{5NN})=\frac{1}{2}$ is recovered with five digits accuracy $p_c(\text{NN})=0.500029(46)$ by averaging over one thousand lattice realisations only.
