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arXiv · 2004.01679

Nonconvex interactions in mean-field spin glasses

Jean-Christophe Mourrat
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Abstract

We propose a conjecture for the limit 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 of 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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Jean-Christophe Mourrat. 2020-04-03. Nonconvex interactions in mean-field spin glasses. https://doi.org/10.2140/pmp.2021.2.61

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