Classical Transport in Disordered Media: Scaling and Effective-Medium Theories

Abstract

Electrical conduction in resistor networks with all but a fraction $p$ of the resistors removed is studied as a paradigm of classical transport in disordered materials. A self-consistent effective-medium theory provides a quantitative description of the model, except in a small critical region, where the scaling law ${\ensuremath{\sigma}}^{\ensuremath{\propto}}{(p\ensuremath{-}{p}_{c})}^{\frac{8}{5}}$ is satisfied (in three dimensions), with ${p}_{c}$ the critical probability for bond percolation. It is also contrasted with a critical-path analysis recently developed for the study of hopping conduction.