Disorder Chaos in the Sherrington-Kirkpatrick Model with External Field

Details Disorder Chaos in the Sherrington-Kirkpatrick Model with External Field Disorder Chaos in the Sherrington-Kirkpatrick Model with External Field

2011-09-15

arxiv.org/abs/1109.3249v1

Mathematics

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39 pages

Scientific paper

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. In the present paper, using Guerra's replica symmetry-breaking bound, we prove that the SK model is also chaotic in the presence of 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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