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We study the multifractal moments of the current distribution in randomlydiluted resistor networks near the percolation treshold. When an externalcurrent 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 ofthe isotropic percolation universality class. By applying our concept of masteroperators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family ofmultifractal exponents $\{\psi_l \}$ for $l \geq 0$ to two-loop order. We findthat our result is in good agreement with numerical data for three dimensions.Comment: 30 pages, 6 figure

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