Malarz Krzysztof
AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Krakow, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):043301. doi: 10.1103/PhysRevE.91.043301. Epub 2015 Apr 7.
In this paper, random-site percolation thresholds for a simple cubic (SC) lattice with site neighborhoods containing next-next-next-nearest neighbors (4NN) are evaluated with Monte Carlo simulations. A recently proposed algorithm with low sampling for percolation thresholds estimation (Bastas et al., arXiv:1411.5834) is implemented for the studies of the top-bottom wrapping probability. The obtained percolation thresholds are p(C)(4NN)=0.31160(12),p(C)(4NN+NN)=0.15040(12),p(C)(4NN+2NN)=0.15950(12),p(C)(4NN+3NN)=0.20490(12),p(C)(4NN+2NN+NN)=0.11440(12),p(C)(4NN+3NN+NN)=0.11920(12),p(C)(4NN+3NN+2NN)=0.11330(12), and p(C)(4NN+3NN+2NN+NN)=0.10000(12), where 3NN, 2NN, and NN stand for next-next-nearest neighbors, next-nearest neighbors, and nearest neighbors, respectively. As an SC lattice with 4NN neighbors may be mapped onto two independent interpenetrated SC lattices but with a lattice constant that is twice as large, the percolation threshold p(C)(4NN) is exactly equal to p(C)(NN). The simplified method of Bastas et al. allows for uncertainty of the percolation threshold value p(C) to be reached, similar to that obtained with the classical method but ten times faster.
在本文中，通过蒙特卡罗模拟评估了具有包含次近邻、次次近邻和次次次近邻（4NN）的格点邻域的简单立方（SC）晶格的随机位点渗流阈值。为了研究上下包裹概率，采用了最近提出的一种用于渗流阈值估计的低采样算法（巴斯塔斯等人，arXiv:1411.5834）。得到的渗流阈值为p(C)(4NN)=0.31160(12)，p(C)(4NN+NN)=0.15040(12)，p(C)(4NN+2NN)=0.15950(12)，p(C)(4NN+3NN)=0.20490(12)，p(C)(4NN+2NN+NN)=0.11440(12)，p(C)(4NN+3NN+NN)=0.11920(12)，p(C)(4NN+3NN+2NN)=0.11330(12)，以及p(C)(4NN+3NN+2NN+NN)=0.10000(12)，其中3NN、2NN和NN分别代表次次近邻、次近邻和近邻。由于具有4NN邻域的SC晶格可以映射到两个独立的相互贯穿的SC晶格上，但晶格常数是原来的两倍，所以渗流阈值p(C)(4NN)恰好等于p(C)(NN)。巴斯塔斯等人提出的简化方法能够达到渗流阈值p(C)的不确定性，与经典方法得到的结果类似，但速度快十倍。
