Local energy approach to the dynamic glass transition

Abstract

We propose a new class of phenomenological models for dynamic glass transitions. The system consists of an ensemble of mesoscopic regions to which local energies are allocated. At each time step, a region is randomly chosen and a new local energy is drawn from a distribution that self-consistently depends on the global energy of the system. Then, the transition is accepted or not according to the Metropolis rule. Within this scheme, we model an energy threshold leading to a mode-coupling glass transition as in the p-spin model. The glassy dynamics is characterized by a two-step relaxation of the energy autocorrelation function. The aging scaling is fully determined by the evolution of the global energy and linear violations of the fluctuation dissipation relation are found for observables uncorrelated with the energies. Interestingly, our mean-field approach has a natural extension to finite dimension, that we briefly discuss.

4 pages, 5 figures

References in corpus (20)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• Direct experimental evidence of a growing length scale accompanying the glass transition
• Glassy dynamics of kinetically constrained models
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Coarse-grained microscopic model of glass formers
• Configurational Entropy and Diffusivity of Supercooled Water
• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Saddles in the energy landscape probed by supercooled liquids
• Aging on Parisi's tree
• Phase space geometry and slow dynamics
• Geometric approach to the dynamic glass transition
• Weak-ergodicity breaking in mean-field spin-glass models
• Quasi-equilibrium interpretation of aging dynamics
• Spatially heterogeneous ages in glassy dynamics
• Role of the unstable directions in the equilibrium and aging dynamics of supercooled liquids
• Fluctuation-dissipation relations and effective temperatures in simple non-mean field systems
• Activated aging dynamics and negative fluctuation-dissipation ratios
• Fluctuation-dissipation relations in trap models
• Microscopic realizations of the Trap Model