Local-field effects in nonlinear dielectrics

In a system of identical nonlinear dielectric inclusions immersed in a uniform linear dielectric medium the mean polarization on a macroscopic length scale is related to the Maxwell field by a nonlocal and nonlinear constitutive equation. The method of statistical averaging and cluster expansion is used to derive a formally exact expression for the constitutive equation. The resulting cluster integrals are shown to be absolutely convergent, i.e., independent of the shape of the macroscopic sample in the thermodynamic limit. For a suspension of spherical inclusions a selection of terms leads to a nonlinear Clausius-Mossotti relation. Expressions are derived for the correlation corrections to this mean-field result.