Self-Consistent Average Green's Function in Random Lattices: A Generalized Coherent-Potential Approximation (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>) and Its Diagrammatic Equivalents

Abstract

We describe a simple generalization of the coherent-potential approximation that is exactly equivalent to the self-contained cumulant expansions and the self-consistent diagrammatic-resummation techniques. A detailed analysis of these different methods for the pair case is given.