Abstract
Using a Ward identity, the equivalence of conventional configurational averaging techniques and a recently developed 'expended space' approach is established within the coherent potential approximation for two-particle properties of a simple model Hamiltonian (arbitrary cellular disorder). It is confirmed that the CPA does not predict Anderson localization on any Cayley tree cactus, although it preserves a degree of anomalous behaviour in the one-dimensional lattice and generally produces vertex corrections that are systematically sensitive to average fluctuations.