A general formulation for the spectral noise $S_R$ of random linear resistor networks of arbitrary topology is given. General calculational methods based on Tellegen’s theorem are illustrated for one- and two-probe configurations. For self-similar networks, we show the existence of a new exponent b, member of a whole new hierarchy of exponents characterizing the size dependence of the normalized noise spectrum ${\mathrm{scrS}}_R$=$S_R$/$R^2$. is shown to lie between the fractal dimension d¯ and the resistance exponent -βsubL. b has been calculated for a large class of fractal structures: Sierpiński gaskets, X lattices, von Koch structures, etc. For percolating systems, scrSsubR is investigated for p<psubc as well as for p>psubc. In particular, an anomalous increase of the noise at p→psubcsup+ is obtained. A finite-size-scaling function is proposed, and the corresponding exponent b is calculated in mean-field theory.

• Received 21 August 1984

DOI:https://doi.org/10.1103/PhysRevA.31.2662