Universality and extremal aging for dynamics of spin glasses on subexponential time scales

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)77-127
Number of pages51
JournalCommunications on Pure and Applied Mathematics
Volume65
Issue number1
DOIs
StatePublished - Jan 2012

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Spin glass
Spin Glass
Universality
Time Scales
Aging of materials
Energy Model
Extremal Process
Time Change
Model
Spin Models
Trap
Converge
Clocks
Range of data

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Universality and extremal aging for dynamics of spin glasses on subexponential time scales. / Ben Arous, Gérard; Gün, Onur.

In: Communications on Pure and Applied Mathematics, Vol. 65, No. 1, 01.2012, p. 77-127.

Research output: Contribution to journalArticle

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