Critical behavior of the weakly nonlinear conductivity and flicker noise of two-component composites

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Abstract
A scaling theory of the weakly nonlinear conductivity and flicker noise near the percolation threshold of a two-component composite is formulated and some of its physical consequences are examined. Both components are assumed to have finite Ohmic conductivities, but with a ratio that is very different from 1. We predict that under certain conditions a nonmonotonic dependence of the weakly nonlinear conductivity on the volume fraction of the good conductor can be observed, with a maximum very near to the threshold and a local minimum somewhat above it. We also predict that, depending on the values of the important physical parameters of the system, either the good conductor or the poor conductor may dominate the critical behavior both above and below the threshold. Some of these predictions are compared with results of numerical simulations on two-dimensional random resistor networks and with an effective-medium approximation (EMA). The numerical results are shown to reproduce some of the predictions of the scaling theory. The EMA is shown to follow the same qualitative behavior but to reproduce poorly the quantitative results.