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Title: Replica symmetry breaking in multi-species spin glasses.

Abstract: There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on [0,1], where the measure represents the similarity (or "overlap") of two independently sampled spin configurations. At high temperatures, the formula's minimum is achieved at a measure which is a point mass, meaning sample configurations are asymptotically orthogonal up to a magnetic field correction. At low temperatures, though, a very different behavior emerges known as replica symmetry breaking (RSB). The deep wells in the energy landscape create more rigid structure, and the optimal overlap measure is no longer a point mass. The exact size of its support remains in many cases an open problem. Here we consider these themes when mean-field models are relaxed to so-called multi-species spin glasses. I will share some results from joint works with Leila Sloman and Youngtak Sohn.

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