Damage spreading in the mode-coupling equations for glasses

TL;DR

This paper investigates damage spreading in the off-equilibrium mode-coupling equations for the spherical p-spin model, revealing a temperature transition that affects the stability of damage over time.

Contribution

It demonstrates the existence of a temperature transition in damage spreading for the spherical p-spin model, a novel insight into non-linear damage dynamics in glassy systems.

Findings

Damage decays to zero above transition temperature T_0

Below T_0, damage stabilizes at a finite value

Transition persists despite asymmetry in interactions

Abstract

We examine the problem of damage spreading in the off-equilibrium mode coupling equations. The study is done for the spherical $p$-spin model introduced by Crisanti, Horner and Sommers. For $p>2$ we show the existence of a temperature transition $T_0$ well above any relevant thermodynamic transition temperature. Above $T_0$ the asymptotic damage decays to zero while below $T_0$ it decays to a finite value independent of the initial damage. This transition is stable in the presence of asymmetry in the interactions. We discuss the physical origin of this peculiar phase transition which occurs as a consequence of the non-linear coupling between the damage and the two-time correlation functions.