CLUSTER SIZE AND BOUNDARY DISTRIBUTION NEAR PERCOLATION THRESHOLD
CLUSTER SIZE AND BOUNDARY DISTRIBUTION NEAR PERCOLATION THRESHOLD
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DOI：
10.1103/physrevb.14.5046
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发表时间：
1976-01-01
影响因子：
3.7
通讯作者：
LEATH, PL
中科院分区：
文献类型：
--
作者：
LEATH, PL
结果表明，形状的大，随机集群，附近的临界渗流浓度c 0，是这样的，它们的平均boundaryis成正比于它们的平均散装< n>，这是说明了一个参数，它表明，尺寸的边界是相同的散装。所得到的比率< n>与临界浓度c 0简单相关。在一个简单的正方形格子上，给出了c< c 0时的蒙特卡罗计算的详细结果，它们给出了概率分布P（n，B）的经验公式，用于找到一个大小为n、边界为B的簇，该簇与B n中的高斯分布成正比，与浓度无关，在B n= α 0，n→∞处缩小为δ函数。高斯形式的渐近行为给出临界指数β= 0.19 ± 0.16，γ= 2.34 ± 0.3，α 0给出临界浓度c0 = 0.5 87 ± 0.14，与以前的测定结果一致。
It is shown that the shape of the large, random clusters, near the critical percolation concentration c 0, is such that their mean boundaryis proportional to their mean bulk< n> and this is illustrated by an argument which shows that the dimension of the boundary is the same as that of the bulk. The resulting ratio< n> is simply related to the critical concentration c 0. The detailed results of a Monte Carlo calculation, previously reported, are given for c< c 0 on a simple square lattice; they yield an empirical formula for the probability distribution P (n, b), for finding a cluster of size n and boundary b, that is proportional to a Gaussian in b n, which is independent of concentration and which narrows to a δ function at b n= α 0, n→∞. The asymptotic behavior of the Gaussian form gives the critical exponents β= 0.19±0.16, and γ= 2.34±0.3, and α 0, gives the critical concentration c 0= 0.587±0.14, in agreement with previous determinations.