  Effects of two-body dipolar interactions on the effective
permittivity/conductivity of a binary, symmetric, random dielectric composite
are investigated in a self-consistent framework. By arbitrarily splitting the
singularity of the Green tensor of the electric field, we introduce an
additional degree of freedom into the problem, in the form of an unknown
"inner" depolarization constant. Two coupled self-consistent equations
determine the latter and the permittivity in terms of the dielectric contrast
and the volume fractions. One of them generalizes the usual Coherent Potential
condition to many-body interactions between single-phase clusters of
polarizable matter elements, while the other one determines the effective
medium in which clusters are embedded. The latter is in general different from
the overall permittivity. The proposed approach allows for many-body
corrections to the Bruggeman-Landauer (BL) scheme to be handled in a
multiple-scattering framework. Four parameters are used to adjust the degree of
self-consistency and to characterize clusters in a schematic geometrical way.
Given these parameters, the resulting theory is "exact" to second order in the
volume fractions. For suitable parameter values, reasonable to excellent
agreement is found between theory and simulations of random-resistor networks
and pixelwise-disordered arrays in two and tree dimensions, over the whole
range of volume fractions. Comparisons with simulation data are made using an
"effective" scalar depolarization constant that constitutes a very sensitive
indicator of deviations from the BL theory.
