NDLI: Low Temperature Asymptotics of Spherical Mean Field Spin Glasses

Content Provider	Springer Nature Link
Author	Jagannath, Aukosh Tobasco, Ian
Copyright Year	2017
Abstract	In this paper, we study the low temperature limit of the spherical Crisanti–Sommers variational problem. We identify the $${\Gamma}$$ -limit of the Crisanti–Sommers functionals, thereby establishing a rigorous variational problem for the ground state energy of spherical mixed p-spin glasses. As an application, we compute moderate deviations of the corresponding minimizers in the low temperature limit. In particular, for a large class of models this yields moderate deviations for the overlap distribution as well as providing sharp interpolation estimates between models. We then analyze the ground state energy problem. We show that this variational problem is dual to an obstacle-type problem. This duality is at the heart of our analysis. We present the regularity theory of the optimizers of the primal and dual problems. This culminates in a simple method for constructing a finite dimensional space in which these optimizers live for any model. As a consequence of these results, we unify independent predictions of Crisanti–Leuzzi and Auffinger–Ben Arous regarding the one-step Replica Symmetry Breaking (1RSB) phase in this limit. We find that the “positive replicon eigenvalue” and “pure-like” conditions are together necessary for optimality, but that neither are themselves sufficient, answering a question of Auffinger and Ben Arous in the negative. We end by proving that these conditions completely characterize the 1RSB phase in 2 + p-spin models.
Starting Page	979
Ending Page	1017
Page Count	39
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	352
Issue Number	3
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2017-03-24
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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