Some examples of quenched self-averaging in models with Gaussian disorder

Wei Kuo Chen, Dmitry Panchenko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we give an elementary approach to several results of Chatterjee in (Disorder chaos and multiple valleys in spin glasses (2013) arXiv:0907.3381, Comm. Math. Phys. 337 (2015) 93-102), as well as some generalizations. First, we prove quenched disorder chaos for the bond overlap in the Edwards-Anderson type models with Gaussian disorder. The proof extends to systems at different temperatures and covers a number of other models, such as the mixed p-spin model, Sherrington-Kirkpatrick model with multi-dimensional spins and diluted p-spin model. Next, we adapt the same idea to prove quenched self-averaging of the bond magnetization for one system and use it to show quenched self-averaging of the site overlap for random field models with positively correlated spins. Finally, we show self-averaging for certain modifications of the random field itself.

Original languageEnglish (US)
Pages (from-to)243-258
Number of pages16
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume53
Issue number1
DOIs
StatePublished - Feb 2017

Keywords

  • Gaussian disorder
  • Self-averaging
  • Spin glasses

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