A theory of conductivity in disordered resistor networks

The use of a perturbation method in the study of percolation problems is examined. The specific case discussed is the conductivity of a disordered square resistor network in which bonds are broken at random (bond model). The formalism used is closely analogous to that used in the study of disordered alloys. A detailed discussion of the properties of the Green functions is given, and numerical results are obtained within a cluster approximation. It is found that, with the smallest possible cluster, a significant improvement over the effective-medium theory is obtained.