Universality of the REM for dynamics of mean-field spin glasses
| dc.creator | Arous, Gerard Ben | |
| dc.creator | Bovier, Anton | |
| dc.creator | Cerny, Jiri | |
| dc.date | 2007-06-14 | |
| dc.date.accessioned | 2026-07-07T08:18:21Z | |
| dc.date.available | 2026-07-07T08:18:21Z | |
| dc.description | We consider a version of a 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 any p>2 and any inverse temperature β>0, there exist constants g>0, such that for all exponential time scales, $\exp(γN)$, with $γ< g$, 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 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. | |
| dc.description | 30 pages, 1 fugre | |
| dc.identifier | https://arxiv.org/abs/0706.2135 | |
| dc.identifier | http://arxiv.org/abs/0706.2135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134402 | |
| dc.subject | Probability | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | 82C44, 60K35, 60G70 | |
| dc.title | Universality of the REM for dynamics of mean-field spin glasses | |
| dc.type | text |