## Abstract

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 γ_{β,p} > 0, such that for all exponential time scales, exp(γ N), with γ < γ_{β,p} , the properly rescaled clock process (time-change process) converges to an α-stable subordinator where α = γ/β^{2} < 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 language | English (US) |
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Pages (from-to) | 663-695 |

Number of pages | 33 |

Journal | Communications In Mathematical Physics |

Volume | 282 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2008 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics