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Nonconvex interactions in
mean-field spin glasses
Jean-Christophe Mourrat |
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Vol. 2 (2021), No. 2, 281–339
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Abstract |
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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. |
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Keywords
spin glass, Hamilton–Jacobi equation, Wasserstein space
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Mathematical Subject Classification
Primary: 82B44, 82D30
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Milestones
Received: 16 April 2020
Revised: 9 December 2020
Accepted: 15 December 2020
Published: 22 May 2021
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Authors |
| Jean-Christophe Mourrat | |
| Courant Institute of Mathematical
Sciences New York University New York, NY United States |
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