Mean Field Spin Glasses. From Parisi to Boltzmann (?)

The Parisi theory makes astounding predictions about the large volume behavior of mean field disordered systems, such as the paradigmatic SK-model. Some of these predictions have been meanwhile rigorously confirmed, yet many most of the deep conceptual puzzles raised by the Parisi theory remain to these days unanswered, in fact: un-addressed. Even a non-rigorous (!) yet hands-on, microcanonical treatment of spin glasses within the Boltzmann-Gibbs framework is to date lacking.

I will discuss these issues, and suggest through a case-study that the proper framework to address them rigorously is provided by the treatment pioneered by Thouless-Anderson-Palmer, and Plefka.

Joint work with David Belius (Zurich).