Slow relaxation, dynamic transitions and extreme value statistics in disordered systems

TL;DR

This paper investigates the dynamics of simple disordered models, revealing a coexistence point between active and inactive phases linked to extreme value statistics of the energy landscape, highlighting dynamic phase transitions.

Contribution

It establishes a connection between dynamic phase transitions in disordered models and the extreme value statistics of their energy landscapes, providing new insights into their behavior.

Findings

Disordered models exhibit a coexistence point between active and inactive phases.

Dynamic phase transitions are related to extreme value statistics.

The models' dynamics are influenced by the energy landscape's extremal properties.

Abstract

We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase transition in these models to the extreme value statistics of the associated random energy landscape.