Universality of the REM for dynamics of mean-field spin glasses
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1241 | |
dc.contributor.author | Ben Arous, Gérard | |
dc.contributor.author | Bovier, Anton | |
dc.contributor.author | Černý, Jiři | |
dc.date.accessioned | 2016-03-24T17:38:16Z | |
dc.date.available | 2019-06-28T08:02:38Z | |
dc.date.issued | 2007 | |
dc.description.abstract | 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 $p geq 3$ and any inverse temperature $beta>0$, there exist constants $g_0>0$, such that for all exponential time scales, $exp(gamma N)$, with $gleq g_0$, the properly rescaled emphclock process (time-change process), converges to an $a$-stable subordinator where $a=g/b^2<1$. Moreover, the dynamics exhibits aging at these time scales with time-time correlation function converging to the arcsine law of this hbox$alpha$-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. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/3441 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1883 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.title | Universality of the REM for dynamics of mean-field spin glasses | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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