论文标题
平方和简单的立方晶格上的现场渗透及其连续限制
Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
论文作者
论文摘要
通过蒙特卡洛模拟，我们研究了具有各种最近邻居组合的正方形和简单的立方格的远程位点渗透，直到第八个邻居，用于方形格子和第九个邻居，用于简单的立方晶格。我们使用单群集生长算法找到了23个系统的精确阈值。在具有紧凑型社区的晶格上的位置渗透可以映射到诸如磁盘和球体等扩展形状的晶格渗透问题，并且阈值可能与这些形状的对象的连续阈值$η_c$有关。该映射意味着$ zp_ {c} \ sim4η_c= 4.51235 $ in 2d和$ zp_ {c} \ sim8η_c= 2.73512 $ in 3d in 3d in 3d in 3d for $ z $分别用于圆形和球形邻域，其中$ z $是$ z $。将我们的数据拟合到表格$ p_c = c/（z+b）$我们找到与$ c = 2^dη_c$的良好协议;常数$ b $代表有限的$ z $更正项。我们还研究阈值的幂律。
By means of Monte Carlo simulations, we study long-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors, up to the eighth neighbors for the square lattice and the ninth neighbors for the simple cubic lattice. We find precise thresholds for 23 systems using a single-cluster growth algorithm. Site percolation on lattices with compact neighborhoods can be mapped to problems of lattice percolation of extended shapes, such as disks and spheres, and the thresholds can be related to the continuum thresholds $η_c$ for objects of those shapes. This mapping implies $zp_{c} \sim 4 η_c = 4.51235$ in 2D and $zp_{c} \sim 8 η_c = 2.73512$ in 3D for large $z$ for circular and spherical neighborhoods respectively, where $z$ is the coordination number. Fitting our data to the form $p_c = c/(z+b)$ we find good agreement with $c = 2^d η_c$; the constant $b$ represents a finite-$z$ correction term. We also study power-law fits of the thresholds.
