Multifractal structure of the incipient infinite percolating cluster

L. de Arcangelis, A. Coniglio, and S. Redner
Phys. Rev. B 36, 5631 – Published 1 October 1987
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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/lnVmax, where V is the voltage across each bond and Vmax 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

Authors & Affiliations

L. de Arcangelis, A. Coniglio, and S. Redner

  • Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215

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Issue

Vol. 36, Iss. 10 — 1 October 1987

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