Nonconvex interactions in mean-field spin glasses

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.

arXiv comment51 pages, final version, to appear in Probab. Math. Phys

References in corpus (8)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Parisi formula has a unique minimizer
• The free energy in a multi-species Sherrington-Kirkpatrick model
• Equilibrium statistical mechanics of bipartite spin systems
• Free energy and complexity of spherical bipartite models
• Free energy in the generalized Sherrington-Kirkpatrick mean field model
• Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique
• Notes on the p-spin glass studied via Hamilton-Jacobi and Smooth-Cavity techniques

Cited by in corpus (3)

• Free energy in multi-species mixed $p$-spin spherical models
• The solution of the deep Boltzmann machine on the Nishimori line
• Hamilton-Jacobi equations from mean-field spin glasses