Classical transport in disordered media: Scaling and effective-medium theories

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 σ(p-pc)85 is satisfied (in three dimensions), with pc the critical probability for bond percolation. It is also contrasted with a critical-path analysis recently developed for the study of hopping conduction.