On the dynamics of Kac $p$-spin glasses

Details On the dynamics of Kac $p$-spin glasses On the dynamics of Kac $p$-spin glasses

2006-04-03

arxiv.org/abs/cond-mat/0604053v1

Journal of Statistical Physics, Vol. 126, Nos. 4/5, February/March 2007

Physics

Condensed Matter

Statistical Mechanics

Submitted to JSP Special Issue on the Cortona Meeting "Mathematical Physics of Spin Glasses", Cortona (Italy), June 27 - July

Scientific paper

10.1007/s10955-006-9196-6

This paper discusses the dynamical properties of $p$-spin models with Kac kind interactions. For large but finite interaction range $R$ one finds two different time scales for relaxation. A first relaxation roughly independent of $R$ where the system is confined to limited regions of the configuration space and an $R$ dependent time scale where the system is able to escape the confining regions. I will argue that the $R$ independent time scales can be described through dynamical mean field theory, while non-perturbative new techniques have to be used to deal with the $R$ dependent scales.

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