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

Abstract

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 $l\ge 0$ to two-loop order. We find that our result is in good agreement with numerical data for three dimensions.

30 pages, 6 figures

References in corpus (4)

• Multifractality in Human Heartbeat Dynamics
• Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters
• Multifractal Properties of the Random Resistor Network
• Master Operators Govern Multifractality in Percolation

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