Abstract
The nonlocal coherent-potential approximation (NLCPA) has recently been introduced for describing short-range correlations in disordered systems, for example short-range ordering e ects in alloys. As a generalisation of the widely-used coherent-potential approximation (CPA), the NLCPA determines an e ective medium via the self-consistent embedding of a cluster with periodic Bornvon Karman boundary conditions imposed. Whilst this approach has the advantageous property of preserving the single-site translational invariance of the underlying lattice, it has recently been shown to yield spurious and non-unique results below some critical cluster size. In this paper we reformulate the NLCPA as a unique and systematic theory and show that the previous formalism is a specific limiting case of the new formulation. We explicitly demonstrate the theory for a one-dimensional tight-binding model in order to compare with exact numerical results.