Polarizability Fluctuations in Dielectric Materials with Quenched Disorder

We study a model of dielectric response for spatially disordered materials. In this model the local polarizability alpha(r) is a quenched random variable. From a one-loop level renormalization-group analysis, we predict that with increasing length scale L, the dimensionless fluctuation strength alpha;sigma, where 1/alpha; and sigma(2) are the average and the variance of the distribution for 1/alpha(r), decays as 1/L(2) universally at large length scales. The interplay of the random polarizability and the long-range dipole-dipole interaction is discussed.