Rigorous construction of the pure states for certain spin glass models

Abstract

For a large class of Gaussian Hamiltonians, that includes the Sherrington–Kirkpatrick model, the p-spin interaction model for even p, and many others, we prove at each temperature (under a very mild and essentially necessary condition) that generically the “pure states” predicted by physics do exist. The configuration space decomposes in an essentially unique manner in a sequence of subsets on which the overlap takes essentially its maximum value. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 346 (2008).