On the dynamics of Kac $p$-spin glasses

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.