On the proof of the Parisi formula by Guerra and Talagrand

Abstract

The Parisi formula is an expression for the limiting free energy of the Sherrington-Kirkpatrick spin glass model, which had first been derived by Parisi using a non-rigorous replica method together with an hierarchical ansatz for the solution of the variational problem. It had become quickly clear that behind the solution, if correct, lies an interesting mathematical structure. The formula has recently been proved by Michel Talagrand based partly on earlier ideas and results by Francesco Guerra. The talk will try to explain why the problem is mathematically interesting, and sketch the ideas of Guerra and Talagrand. It should be emphasized that despite the fact that the formula is proved, many things remain still quite mysterious.