论文标题
在平方晶格上的三角形中渗透
Percolation in a triangle on a square lattice
论文作者
论文摘要
平面上的渗透通常与跨矩形系统相对两侧的簇相关。在这里，我们研究了在平方晶格上产生的三腿簇，并跨越了等边三角形的三个侧面。如果三角形相对于晶格的位置和方向是统一的随机分配的，则获得了确定渗透阈值的有效方法，与为矩形几何形状开发的最先进的蒙特卡洛方法相当。三腿簇的通用交叉概率是与几何学无关的，它为该方法提供了进一步改进的方法。
Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If the position and orientation of the triangles relative to the lattice are uniformly randomized, one obtains an efficient method of determining the percolation threshold, on par with the most advanced Monte Carlo methods developed for the rectangular geometry. The universal crossing probability for three-leg clusters is geometry-independent, which opens a way for further improvements of the method.
