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Effects of two-body dipolar interactions on the effectivepermittivity/conductivity of a binary, symmetric, random dielectric compositeare investigated in a self-consistent framework. By arbitrarily splitting thesingularity of the Green tensor of the electric field, we introduce anadditional degree of freedom into the problem, in the form of an unknown"inner" depolarization constant. Two coupled self-consistent equationsdetermine the latter and the permittivity in terms of the dielectric contrastand the volume fractions. One of them generalizes the usual Coherent Potentialcondition to many-body interactions between single-phase clusters ofpolarizable matter elements, while the other one determines the effectivemedium in which clusters are embedded. The latter is in general different fromthe overall permittivity. The proposed approach allows for many-bodycorrections to the Bruggeman-Landauer (BL) scheme to be handled in amultiple-scattering framework. Four parameters are used to adjust the degree ofself-consistency and to characterize clusters in a schematic geometrical way.Given these parameters, the resulting theory is "exact" to second order in thevolume fractions. For suitable parameter values, reasonable to excellentagreement is found between theory and simulations of random-resistor networksand pixelwise-disordered arrays in two and tree dimensions, over the wholerange of volume fractions. Comparisons with simulation data are made using an"effective" scalar depolarization constant that constitutes a very sensitiveindicator of deviations from the BL theory.

Generalized two-body self-consistent theory of random linear dielectric  composites: an effective-medium approach to clustering in highly-disordered  media