  We sketch a new framework for the analysis of disordered systems, in
particular mean field spin glasses, which is variational in nature and within
the formalism of classical thermodynamics. For concreteness, only the
Sherrington-Kirkpatrick model is considered here. For this we show how the
Parisi solution (replica symmetric, or when replica symmetry is broken)
emerges, in large but finite volumes, from a high temperature expansion to
second order of the Gibbs potential with respect to order parameters encoding
the law of the effective fields. In contrast with classical systems where
convexity in the order parameters is the default situation, the functionals
employed here are, at infinite temperature, concave: this feature is eventually
due to the Gaussian nature of the interaction and implies, in particular, that
the canonical Boltzmann-Gibbs variational principles must be reversed. The
considerations suggest that thermodynamical phase transitions are intimately
related to the divergence of the infinite expansions.
