Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime
Gérard Ben Arousa b✉, Eliran Subaga c, Ofer Zeitounid e f g
- aCourant Institute, 251 Mercer St. New York NY 10012 USA
- bNYU‐Shanghai, 1555 Century Ave. Shanghai 200122 P.R. China
- cCourant Institute 251 Mercer St., New York NY 10012 USA
- dDepartment of Mathematics, Weizmann Institute Rehovot 76100 Israel
- eDepartment of Mathematics
- fWeizmann Institute
- gRehovot 76100 Israel
- ✉Corresponding author
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Abstract
We study the Gibbs measure of mixed spherical p ‐spin glass models at low temperature, in (part of) the 1‐RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius , where is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models. © 2019 Wiley Periodicals, Inc.