Analytic approximations for disordered systems

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Abstract
Many suggested approximations for the ensemble averaged Green function of a disordered system are not analytically acceptable. Here Kraichnan's (1961) idea of using 'realizable' approximations is explored and generalized. The method is used to prove that a self-consistent cluster multiple scattering approximation in the theory of disordered alloys is analytic, a result which is of both practical and conceptual importance.