Self-Consistent Cluster Theory of Disordered Alloys

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Abstract
Several techniques for extending the single-site coherent-potential approximation (CPA) to account for particular local configurations of atoms are evaluated. It is shown that if one attempts to define a site-diagonal medium by requiring consistency between the Green's function evaluated at the center of the cluster and the external medium, one may obtain unphysical results. If, however, one requires consistency between a site at the boundary and the medium, one can obtain (at least in one dimension) a site-diagonal medium which reproduces the cellular CPA exactly.