Efficient Monte Carlo algorithm and high-precision results for percolation
Efficient Monte Carlo algorithm and high-precision results for percolation
复制标题
DOI：
10.1103/physrevlett.85.4104
复制
发表时间：
2000-11-06
影响因子：
8.6
通讯作者：
Ziff, RM
中科院分区：
文献类型：
--
作者：
Newman, MEJ;Ziff, RM
提出了一种新的Monte Carlo算法，用于研究任意晶格上的位渗流或键渗流。该算法使我们能够计算数量，如集群大小分布或跨越概率在整个范围内的网站或债券占用概率从零到一在一个单一的运行，这需要大量的时间缩放与网格上的网站的数量线性。我们用我们的算法确定了正方形格子上的点渗流在p（c）= 0.59274621（13）处发生渗流跃迁，并对生成概率函数中的4/3次方拉伸指数尾提供了清晰的数值确认。
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at p(c) = 0.592 746 21(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.