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Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime
Author(s) -
Arous Gérard Ben,
Subag Eliran,
Zeitouni Ofer
Publication year - 2020
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21875
Subject(s) - spin glass , measure (data warehouse) , hamiltonian (control theory) , gibbs measure , mathematics , pairwise comparison , radius , point (geometry) , statistical physics , geometry , condensed matter physics , physics , mathematical analysis , statistics , computer security , computer science , mathematical optimization , database
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 N ρ * , where ρ * 2 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.