Multi-Species Spin Glass Models at Critical Temperature

Speaker: Elizabeth Collins-Woodfin (McGill University)

Date: 4/8/25

Abstract: One of the fascinating phenomena in spin glasses is the dramatic change in behavior between the high- and low-temperature regimes. In this talk, we focus on spin glasses near the critical temperature threshold and present results on the fluctuations of the free energy. We examine two variants of the famous Sherrington-Kirkpatrick (SK) model. For the bipartite spherical SK (BSSK) model, we show that the free energy fluctuations at critical temperature converge to a sum of Gaussian and Tracy-Widom distributions, interpolating between known results in the high- and low-temperature regimes. For the multi-species SK (MSK) model (with a positive semi-definite interaction), we provide a sharper variance bound than previously known. The techniques used to study these two models differ significantly, as BSSK has continuous spins, while MSK has discrete spins. We will highlight the key strategies for analyzing each model and discuss some statistical applications.