Fluctuations of the free energy in the mixed p-spin models with external field

Wei Kuo Chen, Partha Sarathi Dey, Dmitry Panchenko

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the free energy in the mixed p-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincaré inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd p-spin interactions for p⩾ 3 , we prove the central limit theorem for the free energy at any temperature and give an explicit formula for the limiting variance. Although we only deal with the case of Ising spins, all our results can be extended to the spherical models as well.

Original languageEnglish (US)
Pages (from-to)41-53
Number of pages13
JournalProbability Theory and Related Fields
Volume168
Issue number1-2
DOIs
StatePublished - Jun 1 2017

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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