Pseudofermion approach to binary disordered systems. I. Effective-medium theories and the augmented-space method

Abstract

A method is developed by which the self-energy rather than the Green's function of a substitutionally disordered system can be directly expressed in terms of augmented-space paths. The method is useful both for systems with diagonal and with off-diagonal disorder. It is shown that Mills' recently proposed modified cumulant expansion and his analytic n-cluster generalizations of the coherent-potential approximations for systems with diagonal disorder can be straightforwardly derived by resumming those augmented-space paths with, at most, n pseudofermions at once in a skeleton self-energy graph. Also, the way to make analytic n-cluster generalizations of the expansion of Blackman, Esterling, and Berk for their model of off-diagonal disorder is indicated.