Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution

Olaf Stenull, Hans-Karl Janssen

Published 2000-07-07, updated 2001-03-13Version 3

We study the multifractal moments of the current distribution in randomly diluted resistor networks near the percolation treshold. When an external current is applied between to terminals $x$ and $x^\prime$ of the network, the $l$th multifractal moment scales as $M_I^{(l)} (x, x^\prime) \sim | x - x^\prime |^{\psi_l /\nu}$, where $\nu$ is the correlation length exponent of the isotropic percolation universality class. By applying our concept of master operators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family of multifractal exponents $\{\psi_l \}$ for $l \geq 0$ to two-loop order. We find that our result is in good agreement with numerical data for three dimensions.