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 macroscop ic length scale is related to the Maxwell field by a nonlocal and nonl inear constitutive equation. The method of statistical averaging and c luster expansion is used to derive a formally exact expression for the constitutive equation. The resulting cluster integrals are shown to b e absolutely convergent, i.e., independent of the shape of the macrosc opic 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.