Resistance fluctuations in random resistor networks above and below the percolation threshold

Abstract

We examine the critical behavior of resistance fluctuations in random resistor networks near a percolation threshold. The ``links-nodes-blobs'' picture is used to discuss a conductor-insulator mixture above the percolation threshold of the conducting bonds. A similar picture is used to discuss a normal-conductor--superconductor mixture below the percolation threshold of the superconducting bonds. Upper and lower bounds are found for the critical behavior in each case. An exact relation is found between the two types of behavior in the case of two-dimensional networks.