Bond percolation processes in d dimensions
Bond percolation processes in d dimensions
复制标题
d 维中的键渗过程
DOI：
10.1088/0305-4470/11/7/025
复制
发表时间：
1978
期刊：
影响因子：
--
通讯作者：
H. Ruskin
中科院分区：
文献类型：
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作者：
D. S. Gaunt;H. Ruskin
研究了d维简单超立方晶格上的键渗流过程。分别通过五阶和四阶导出平均聚类数K（p）和平均聚类大小S（p）的1/ sigma幂的精确展开式，其中sigma =2d-1且p<pc。零阶项是Bethe近似。发现临界概率pc具有展开式，可能是渐近的，pc= sigma-1（1 +21/2 sigma-2 + 71/2 sigma-3 + 57 sigma-4 +...），而簇生长参数λ可以展开为λ = λ B（1-2 σ-2-.）其中lambda B是lambda的Bethe近似。他们还提出了一系列数据的平均集群大小和集群的增长函数为d=4至7。数值分析表明，临界尺寸，直流，为债券渗流直流=6，因为它似乎是网站的问题。证据也支持的猜想，在一个给定的维度上的一个特定的临界指数的值是相同的债券和网站的过程。
The authors study bond percolation processes on a d-dimensional simple hypercubic lattice. Exact expansions for the mean number of clusters, K(p), and the mean cluster size, S(p), in powers of 1/ sigma , where sigma =2d-1 and p<pc, are derived through fifth and fourth order, respectively. The zeroth-order terms are the Bethe approximations. The critical probability pc is found to have the expansion, probably asymptotic, pc= sigma -1(1+21/2 sigma -2+71/2 sigma -3+57 sigma -4+...), while the cluster growth parameter lambda can be expanded as lambda = lambda B(1-2 sigma -2-...) where lambda B is the Bethe approximation for lambda . They also present series data for the mean cluster size and the cluster growth function for d=4 to 7. Numerical analysis suggests that the critical dimension, dc, for bond percolation is dc=6, as it seems to be for the site problem. The evidence also supports the conjecture that the value of a particular critical exponent in a given dimension is the same for both bond and site processes.