Thermodynamic Consistency of the Dynamical Mean-Field Theory of the   Double-Exchange Model
  Although diagrammatic perturbation theory fails for the dynamical-mean field theory of the double-exchange model, the theory is nevertheless Phi-derivable and hence thermodynamically consistent, meaning that the same thermodynamic properties are obtained from either the partition function or the Green's function. We verify this consistency by evaluating the magnetic susceptibility and Curie temperature for any Hund's coupling. 
Randy S. Fishman (Oak Ridge Nat. Lab), Juana Moreno (Univ. North   Dakota), Thomas Maier (Oak Ridge Nat. Lab), and Mark Jarr...