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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.Comment: Published in at http://dx.doi.org/10.1214/12-AOP793 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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