The generalized Parisi formula (Q1408242)

This note announces a long awaited and very remarkable result, namely the validity of a certain variational description (first formulated by G. Parisi) of the free energy per site for a whole class of Gaussian mean field spin glasses containing the Sherrington-Kirkpatrick model and the \(p\)-spin interaction models for \(p\) even. The proof is described as building upon Guerra's interpolation scheme as introduced by \textit{F. Guerra} [Commun. Math. Phys. 233, 1-12 (2003; Zbl 1013.82023)], together with some far-reaching refinements of some of the methods developed by \textit{M. Talagrand} [Spin glasses: A challenge for mathematicans. Cavity and mean field models. Berlin: Springer (2003; Zbl 1033.82002)]. To quote the author: ``\dots even though there is quite a distance between Theorem 1.1 and a complete mathematical understanding of the SK model, one can now hope that it is only a matter of time and work until this understanding is reached''.