Universality and superuniversality of multifractals in nonlinear resistor networks

Abstract

The multifractal functionf(α) is generalized to describe noisy nonlinear random resistor networks. An approximant function for the family of noise exponents is introduced that provides a good description of real percolative systems for strong nonlinearities. By mapping from this family to the multifractal function, one can approximate the latter. A scale transformation of α in the approximation makes the multifractal function universal for all nonlinearities and by applying an additional transformation, this function becomes superuniversal, i.e., independent of the dimension. The universality is demonstrated for the Mandelbrot-Given structure and the implications of these results are discussed on real percolative systems.