Dielectric response of a polarizable system with quenched disorder

We present and analyze a lattice model of a disordered dielectric material. In the model, the local polarizability is a quenched statistical variable. Using a reaction field approach, the dielectric response of the model can be cast in terms of an effective Hamiltonian for a finite primary system coupled to its effective average medium determined self-consistently. A real space renormalization group analysis is carried out by recursively increasing the size of the primary system. The analysis determines the length scale dependence of the local polarizability distribution. For the case of isotropic disorder considered in this paper, we show that the width of the distribution decays algebraically with increasing lattice spacing. We also compute the distribution of solvation and reorganization energies pertinent to kinetics of electron transfer.