Universality of the REM for dynamics of mean-field spin glasses

Gérard Ben Arous, Anton Bovier, Jiří Černý

Research output: Contribution to journalArticlepeer-review


We consider a version of Glauber dynamics for a p-spin Sherrington- Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the N-dimensional hypercube. We show that, for all p ≥ 3 and all inverse temperatures β > 0, there exists a constant γβ,p > 0, such that for all exponential time scales, exp(γ N), with γ < γβ,p , the properly rescaled clock process (time-change process) converges to an α-stable subordinator where α = γ/β2 < 1. Moreover, the dynamics exhibits aging at these time scales with a time-time correlation function converging to the arcsine law of this α-stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system) the dynamics of p-spin models ages in the same way as the REM, and by extension Bouchaud's REM-like trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case p = 2) seems to belong to a different universality class.

Original languageEnglish (US)
Pages (from-to)663-695
Number of pages33
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Sep 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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