Disorder chaos in the sherrington-kirkpatrick model with external field

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Abstract

We consider a spin system obtained by coupling two distinct Sherrington- Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the overlap under the corresponding Gibbs measure is essentially concentrated at a single value. In the absence of external field, this statement was first confirmed by Chatterjee [Disorder chaos and multiple valleys in spin glasses (2009) Preprint]. In the present paper, using Guerra's replica symmetry breaking bound, we prove that the SK model is also chaotic in the presence of the external field and the position of the overlap is determined by an equation related to Guerra's bound and the Parisi measure.

Original languageEnglish (US)
Pages (from-to)3345-3391
Number of pages47
JournalAnnals of Probability
Volume41
Issue number5
DOIs
StatePublished - Oct 10 2013

Keywords

  • Disorder chaos
  • Guerra's replica symmetry breaking bound
  • Parisi formula
  • Parisi measure
  • Sherrington-Kirkpatrick model.

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