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

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.

References in corpus (12)

• Models of traps and glass phenomenology
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Universality Classes for Extreme Value Statistics
• Thermodynamic formalism for systems with Markov dynamics
• Space-time Thermodynamics of the Glass Transition
• Aging on Parisi's tree
• Absence of Thermodynamic Phase Transition in a Model Glass Former
• Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems
• Aging in the random energy model
• ON A DYNAMICAL MODEL OF GLASSES
• Universal dependence of the fluctuation-dissipation ratio on the transition rates in trap models

Cited by in corpus (7)

• Simulating rare events in dynamical processes
• Second-order dynamic transition in a p=2 spin-glass model
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Large Deviations for the density and the current in Non-Equilibrium-Steady-States on disordered rings
• Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media