Deng Youjin, Blöte Henk W J
Laboratory of Material Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016126. doi: 10.1103/PhysRevE.72.016126. Epub 2005 Jul 21.
We investigate the site-percolation problem on the square and simple-cubic lattices by means of a Monte Carlo algorithm that in fact simulates systems with size L(d-1) x infinity, where L specifies the linear system size. This algorithm can be regarded either as an extension of the Hoshen-Kopelman method or as a special case of the transfer-matrix Monte Carlo technique. Various quantities, such as the magnetic correlation function, are sampled in the finite directions of the above geometry. Simulations are arranged such that both bulk and surface quantities can be sampled. On the square lattice, we locate the percolation threshold at p(c) =0.592 746 5 (4) , and determine two universal quantities as Q(gbc) =0.930 34 (1) and Q(gsc) =0.793 72 (3) , which are associated with bulk and surface correlations, respectively. These values agree well with the exact values 2(-5/48) and 2(-1/3) , respectively, which follow from conformal invariance. On the simple-cubic lattice, we locate the percolation threshold at p(c) =0.311 607 7 (4) . We further determine the bulk thermal and magnetic exponents as y(t) =1.1437 (6) and y(h) =2.5219 (2) , respectively, and the surface magnetic exponent at the ordinary phase transition as y (o)(hs) =1.0248 (3) .
我们通过一种蒙特卡罗算法研究正方形和简单立方晶格上的位点渗流问题，该算法实际上模拟的是尺寸为(L(d - 1)×\infty)的系统，其中(L)指定了线性系统的大小。此算法既可以看作是霍申 - 科普曼方法的扩展，也可以看作是转移矩阵蒙特卡罗技术的一个特殊情况。在上述几何结构的有限方向上对各种量进行采样，如磁关联函数。模拟的安排使得体相和表面的量都能被采样。在正方形晶格上，我们确定渗流阈值为(p(c) = 0.5927465(4))，并确定两个普适量，分别为与体相和表面关联相关的(Q(gbc) = 0.93034(1))和(Q(gsc) = 0.79372(3))。这些值分别与共形不变性得出的精确值(2^{(-5/48)})和(2^{(-1/3)})非常吻合。在简单立方晶格上，我们确定渗流阈值为(p(c) = 0.3116077(4))。我们进一步分别确定体相热指数和磁指数为(y(t) = 1.1437(6))和(y(h) = 2.5219(2))，以及在普通相变处的表面磁指数为(y^{(o)}(hs) = 1.0248(3))。
