Diagrammatic approach proposed many years ago for strong correlated Hubbardmodel is developed for analyzing of the thermodynamic potential properties. Thenew exact relation between such renormalized quantities as thermodynamicpotential, one-particle propagator and correlation function is established.This relation contains additional integration of the one-particle propagator bythe auxiliary constant. The vacuum skeleton diagrams constructed fromirreducible Green's functions and tunneling propagator lines are determined andspecial functional is introduced. The properties of such functional areinvestigated and its relation to the thermodynamic potential is established.The stationary properties of this functional with respect to first orderchanging of the correlation function is demonstrated and as a consequence thestationary properties of the thermodynamic potential is proved.
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