Reformulation of the nonlocal coherent-potential approximation as a unique reciprocal-space theory of disorder

The nonlocal coherent-potential approximation (NLCPA) has recently been introduced for describing shortrange correlations in disordered systems, and has been used to study short-range-ordering effects in alloys. However, it has recently been shown to yield spurious and nonunique results for small cluster sizes used in the calculation (with such features gradually disappearing as the cluster size increases). In this paper we reformulate the NLCPA as a unique and systematic theory. The formalism is based upon averaging the (phase-dependent) Green's function over all possible choices of phase. As a consequence, a fully continuous self-energy and spectral function are obtained for all cluster sizes. We show that the previous formalism is a specific limiting case of the reformulation, and explicitly demonstrate the theory for a one-dimensional tight-binding model in order to compare with exact numerical results.