NDLI: Parisi Formula, Disorder Chaos and Fluctuation for the Ground State Energy in the Spherical Mixed p-Spin Models

Content Provider	Springer Nature Link
Author	Chen, Wei Kuo Sen, Arnab
Copyright Year	2016
Abstract	We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for the limiting free energy in the spherical model. As an application, we obtain explicit formulas for the limiting ground state energy in the replica symmetry, one level of replica symmetry breaking and full replica symmetry breaking phases at zero temperature. In addition, our approach leads to new results on disorder chaos in spherical mixed even p-spin models. In particular, we prove that when there is no external field, the location of the ground state energy is chaotic under small perturbations of the disorder. We also establish that in the spherical mixed even p-spin model, the ground state energy superconcentrates in the absence of external field, while it obeys a central limit theorem if the external field is present.
Starting Page	129
Ending Page	173
Page Count	45
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	350
Issue Number	1
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-12-07
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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