Effective-medium theories for site-disordered resistance networks

We develop and discuss different effective-medium theories (EMT's) for the calculation of the conductivity of site-disordered resistance networks. Our EMT's are based on certain treatments of a cluster of bonds and thus take into account at least part of the correlations between the values of bonds with a common site. Comparison is made with exact results for limiting situations and with Monte Carlo calculations. A general cluster EMT and a "disturbed neighborhood" treatment are shown to give a substantial improvement over the usual single-bond EMT that neglects all correlations between the values of different bonds. For dilute and quasidilute systems a low-concentration cluster EMT gives extremely accurate results over the whole range of concentrations, except in critical regions of dilute systems.