Scale invariance in percolation theory and fractals

被引：5

作者：

Entin, MV ^{[1
]}

Entin, GM ^{[1
]}

机构：

[1] NOVOSIBIRSK STATE UNIV,NOVOSIBIRSK 630090,RUSSIA

来源：

JETP LETTERS | 1996年 / 64卷 / 06期

关键词：

D O I：

10.1134/1.567213

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot transformation, leading to a fractal behavior of the percolation probability in the complex plane. The hierarchical chains of impedances, reducing to a nonlinear mapping of the impedance space onto itself, are studied. An infinite continuation of the procedure leads to a fixed point. It is shown that the number of steps required to reach a neighborhood of this point has a fractal distribution. (C) 1996 American Institute of Physics.

引用

页码：467 / 472

页数：6