论文标题
与复杂邻里的蜂窝晶格上的随机位点渗透
Random site percolation on honeycomb lattices with complex neighborhoods
论文作者
论文摘要
我们提出了一个粗略的估计 - 基于缩放假设以及属于最大群集与职业概率的概率，最多可达四个重要的数字 - 对蜂窝状晶格上随机位点渗透问题的关键职业概率与蜂窝状晶格的关键占用概率，该蜂窝质量具有复杂的邻域，该邻里含有复杂的邻里，该邻居包含位于第五位配置区域。有31个这样的社区，其半径范围从一到三个，其中3到24个地点。对于二维常规晶格，具有紧凑的扩展范围社区，在社区中大量$ z $的限制中，网站启用阈值$ p_c $遵循依赖关系$ p_c \ popto 1/z $，最近由Xun，hao和Ziff [物理评论E 105，024105（202222222222）]相反，由于渗透阈值的堕落（$ p_c $的几个值对应于相同数量的$ z $ z $ z $），因此，由于渗透阈值的堕落而摧毁了这种依赖性。单值索引$ζ= \ sum_i z_i r_i $ - 其中$ z_i $和$ r_i $的一个示例是$ i $ th协调区的站点和半径，分别表征了社区并避免避免上述退化。获得的渗透阈值遵循反平方根依赖性$ p_c \ propto 1/\sqrtζ$。还介绍了Newman和Ziff算法的基本社区（针对唯一协调区）的功能边界（编写C）[物理评论E 64，016706（2001）]。
We present a rough estimation -- up to four significant digits, based on the scaling hypothesis and the probability of belonging to the largest cluster vs. the occupation probability -- of the critical occupation probabilities for the random site percolation problem on a honeycomb lattice with complex neighborhoods containing sites up to the fifth coordination zone. There are 31 such neighborhoods with their radius ranging from one to three and containing from three to 24 sites. For two-dimensional regular lattices with compact extended-range neighborhoods, in the limit of the large number $z$ of sites in the neighborhoods, the site percolation thresholds $p_c$ follow the dependency $p_c\propto 1/z$, as recently shown by Xun, Hao and Ziff [Physical Review E 105, 024105 (2022)]. On the contrary, noncompact neighborhoods (with holes) destroy this dependence due to the degeneracy of the percolation threshold (several values of $p_c$ corresponding to the same number $z$ of sites in the neighborhoods). An example of a single-value index $ζ=\sum_i z_i r_i$ -- where $z_i$ and $r_i$ are the number of sites and radius of the $i$-th coordination zone, respectively -- characterizing the neighborhood and allowing avoiding the above-mentioned degeneracy is presented. The percolation threshold obtained follows the inverse square root dependence $p_c\propto 1/\sqrtζ$. The functions boundaries() (written in C) for basic neighborhoods (for the unique coordination zone) for the Newman and Ziff algorithm [Physical Review E 64, 016706 (2001)] are also presented.
