Abstract
By analyzing the voltage distribution of a random resistor network, we show that the backbone of the percolating cluster can be partitioned into an infinity of subsets, each one characterized by a fixed value of x≡lnV/ln, where V is the voltage across each bond and is its maximum value. Each subset is characterized by a distinct value of the fractal dimension φ(x), and as a consequence an infinite set of order parameters is required to describe the backbone structure. A new scaling approach and a real-space renormalization-group treatment are presented to treat the novel aspects of this problem. The mechanism for multifractality based on an underlying multiplicative process is illustrated on a hierarchical model.
- Received 2 April 1987
DOI:https://doi.org/10.1103/PhysRevB.36.5631
©1987 American Physical Society