Narrow Results

In [11], Talagrand gave a rigorous proof of the Parisi formula in the classical Sherrington–Kirkpatrick (SK) model. In this paper, we build upon the methodology developed in [11] and extend Talagrand's result to the class of SK type models in which the spins have arbitrary prior distribution on a bounded subset of the real line.

Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorization rules for the overlap distribution. A comparison between the state of the art for mean field and finite dimensional models is shortly discussed.