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September 2013 Disorder chaos in the Sherrington–Kirkpatrick model with external field
Wei-Kuo Chen
Ann. Probab. 41(5): 3345-3391 (September 2013). DOI: 10.1214/12-AOP793


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.


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Wei-Kuo Chen. "Disorder chaos in the Sherrington–Kirkpatrick model with external field." Ann. Probab. 41 (5) 3345 - 3391, September 2013.


Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1303.60089
MathSciNet: MR3127885
Digital Object Identifier: 10.1214/12-AOP793

Primary: 60K35 , 82B44

Keywords: Disorder chaos , Guerra’s replica symmetry breaking bound , Parisi formula , Parisi measure , Sherrington–Kirkpatrick model

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 5 • September 2013
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