Evidence of a Critical time in Constrained Kinetic Ising models

TL;DR

This paper identifies a critical time in the dynamics of a constrained kinetic Ising model, marking a transition from fast relaxation without aging to slow aging behavior, aligning with experimental observations in fragile glasses.

Contribution

It demonstrates the existence of a critical time in the model's relaxational dynamics, highlighting a transition in relaxation behavior not previously characterized.

Findings

Existence of a critical time separating different relaxation regimes

Fast exponential relaxation without aging before the critical time

Slow relaxation with aging effects after the critical time

Abstract

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.