The Annals of Probability
- Ann. Probab.
- Volume 41, Number 5 (2013), 3345-3391.
Disorder chaos in the Sherrington–Kirkpatrick model with external field
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.
Ann. Probab., Volume 41, Number 5 (2013), 3345-3391.
First available in Project Euclid: 12 September 2013
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Chen, Wei-Kuo. Disorder chaos in the Sherrington–Kirkpatrick model with external field. Ann. Probab. 41 (2013), no. 5, 3345--3391. doi:10.1214/12-AOP793. https://projecteuclid.org/euclid.aop/1378991842