On the dynamics of Kac $p$-spin glasses

TL;DR

This paper explores the dynamical behavior of Kac p-spin glasses, identifying two relaxation time scales and proposing theoretical approaches to describe each, highlighting the complexity of their dynamics.

Contribution

It introduces a distinction between R-independent and R-dependent relaxation scales in Kac p-spin glasses and suggests methods to analyze each regime.

Findings

Two distinct relaxation time scales identified

R-independent scales described by dynamical mean field theory

R-dependent scales require non-perturbative techniques

Abstract

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.