Logarithmic corrections to scaling in critical percolation and random resistor networks.
Logarithmic corrections to scaling in critical percolation and random resistor networks.
复制标题
对临界渗透和随机电阻网络中的缩放进行对数校正。
DOI：
10.1103/physreve.68.036129
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
H. Janssen
中科院分区：
文献类型：
--
作者：
O. Stenull;H. Janssen
我们研究了六维渗流的各种几何性质和输运性质的临界行为。利用场论和重整化群方法，我们分析了涨落引起的对数修正，使之达到并包含了次前序修正。我们的研究理解了渗流关联函数，即两个给定点相连的概率，以及一些描述渗流团簇的分形质量。具体地说，我们计算主干的质量、红键和最短路径。此外，我们还研究了以随机电阻网络为代表的渗流的关键输运性质。我们研究了平均两点电阻以及电流分布的全族多重分形矩。
We study the critical behavior of various geometrical and transport properties of percolation in six dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up to and including the next-to-leading order correction. Our study comprehends the percolation correlation function, i.e., the probability that two given points are connected, and some of the fractal masses describing percolation clusters. To be specific, we calculate the mass of the backbone, the red bonds, and the shortest path. Moreover, we study key transport properties of percolation as represented by the random resistor network. We investigate the average two-point resistance as well as the entire family of multifractal moments of the current distribution.