Equilibrium and Aging Dynamics of Simple Models for Glasses

TL;DR

This paper investigates the energy landscape and aging dynamics of finite-size p-spin models, demonstrating their relevance to real super-cooled liquids and the glass transition, especially near the critical point.

Contribution

It shows that finite-size p-spin models exhibit realistic aging and activated processes, bridging the gap between theoretical models and experimental glassy behavior.

Findings

Finite-size p-spin models display properties of real super-cooled liquids.

Activated processes occur in finite-size models near the glass transition.

Models support the use of p-spin models for studying the glass transition.

Abstract

We analyze the properties of the energy landscape of {\it finite-size} fully connected $p$-spin-like models. In the thermodynamic limit the high temperature phase is described by the schematic Mode Coupling Theory of super-cooled liquids. In this limit the barriers between different basins are infinite below the critical dynamical temperature the ergodicity is broken on in infinite times. We show that {\it finite-size} fully connected $p$-spin-like models, where activated processes are possible, do exhibit properties typical of real super-cooled liquid when both are near the critical glass transition. Our results support the conclusion that fully-connected $p$-spin-like models are the natural statistical mechanical models for studying the glass transition in super-cooled liquids.