Vol. 2, No. 2, 2021

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Nonconvex interactions in mean-field spin glasses

Jean-Christophe Mourrat

Vol. 2 (2021), No. 2, 281–339

We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite structure, and show that the conjectured limit is an upper bound. The conjectured limit is described in terms of the solution to an infinite-dimensional Hamilton–Jacobi equation. A fundamental difficulty of the problem is that the nonlinearity in this equation is not convex. We also question the possibility to characterize this conjectured limit in terms of a saddle-point problem.

spin glass, Hamilton–Jacobi equation, Wasserstein space
Mathematical Subject Classification
Primary: 82B44, 82D30
Received: 16 April 2020
Revised: 9 December 2020
Accepted: 15 December 2020
Published: 22 May 2021
Jean-Christophe Mourrat
Courant Institute of Mathematical Sciences
New York University
New York, NY
United States