Generalization of the coherent-potential approximation to systems with bond randomness

We present a generalization of the single-site coherent-potential approximation (CPA) which allows the calculation of the density of states (DOS) of random-bond-disordered systems, such as polymer systems and disordered resistor networks. This generalization preserves the desirable properties of the CPA, such as uniqueness, analyticity, and the satisfaction of fundamental DOS sum rules. Numerical results indicate that this new approach yields DOS's which (i) faithfully represent the exact DOS in the limit of systems consisting of a single bond (pure systems), and (ii) properly interpolate between the structure in the DOS which is caused by disorder away from that limit. Possible applications of the theory to the calculation of the DOS of nonrandom-bond-disordered systems, as well as the calculation of the transport properties of such systems, are discussed.