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Universality and extremal aging for dynamics of spin glasses on subexponential time scales
Article first published online: 2 MAY 2011
DOI: 10.1002/cpa.20372
Copyright © 2011 Wiley Periodicals, Inc.
1097-0312/asset/cover.gif?v=1&s=27e2b2132052ff78aa82eddfab7608281350adb9 "Communications on Pure and Applied Mathematics")
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How to Cite
Ben Arous, G. and Gün, O. (2012), Universality and extremal aging for dynamics of spin glasses on subexponential time scales. Comm. Pure Appl. Math., 65: 77–127. doi: 10.1002/cpa.20372
Publication History
- Issue published online: 18 OCT 2011
- Article first published online: 2 MAY 2011
- Manuscript Received: OCT 2010
- Abstract
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Abstract
We consider random hopping time (RHT) dynamics of the Sherrington-Kirkpatrick (SK) model and p-spin models of spin glasses. For any of these models and for any inverse temperature β > 0 we prove that, on time scales that are subexponential in the dimension, the properly scaled clock process (time-change process) of the dynamics converges to an extremal process. Moreover, on these time scales, the system exhibits aging-like behavior, which we call extremal aging. In other words, the dynamics of these models ages as the random energy model (REM) does. Hence, by extension, this confirms Bouchaud's REM-like trap model as a universal aging mechanism for a wide range of systems that, for the first time, includes the SK model. © 2011 Wiley Periodicals, Inc.