Random matrices and complexity of spin glasses

Antonio Auffinger, Gérard Ben Arous, Jiří Černý

Research output: Contribution to journalArticle

Abstract

We give an asymptotic evaluation of the complexity of spherical p-spin spin glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum (the ground state), and the other local minima, and describe an interesting layered structure of the low critical values for the Hamiltonians of these models. We also show that our approach allows us to compute the related TAPcomplexity and extend the results known in the physics literature. As an independent tool, we prove a large deviation principle for the k th-largest eigenvalue of the Gaussian orthogonal ensemble, extending the results of Ben Arous, Dembo, and Guionnet.

Original languageEnglish (US)
Pages (from-to)165-201
Number of pages37
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number2
DOIs
StatePublished - Feb 2013

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Spin glass
Spin Glass
Random Matrices
Hamiltonians
Energy Landscape
Large Deviation Principle
Random Matrix Theory
Largest Eigenvalue
Local Minima
Ground state
Ground State
Critical value
Ensemble
Physics
Evaluation
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Random matrices and complexity of spin glasses. / Auffinger, Antonio; Arous, Gérard Ben; Černý, Jiří.

In: Communications on Pure and Applied Mathematics, Vol. 66, No. 2, 02.2013, p. 165-201.

Research output: Contribution to journalArticle

Auffinger, Antonio ; Arous, Gérard Ben ; Černý, Jiří. / Random matrices and complexity of spin glasses. In: Communications on Pure and Applied Mathematics. 2013 ; Vol. 66, No. 2. pp. 165-201.
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