From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks

Abstract

Trap models describe glassy dynamics as a stochastic process on a network of configurations representing local energy minima. We study within this class the paradigmatic Barrat-Mézard model, which has Glauber transition rates. Our focus is on the effects of the network connectivity, where we go beyond the usual mean field (fully connected) approximation and consider sparse networks, specifically random regular graphs. We obtain the spectral density of relaxation rates of the master operator using the cavity method, revealing very rich behaviour as a function of network connectivity $c$ and temperature $T$. We trace this back to a crossover from initially entropic barriers, resulting from a paucity of downhill directions, to energy barriers that govern the escape from local minima at long times. The insights gained are used to rationalize the relaxation of the energy after a quench from high $T$, as well as the corresponding correlation and persistence functions.

Accepted version for publication in "Journal of Statistical Mechanics: Theory and Experiment". 42 pages , 9 figures, 7 appendices

References in corpus (7)

• Introduction to Random Matrices - Theory and Practice
• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Spectra of Sparse Random Matrices
• On the localization transition in symmetric random matrices
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Activated Aging Dynamics and Effective Trap Model Description in the Random Energy Model
• Spectral characterization of aging: the rem-like trap model

Cited by in corpus (8)

• Revisiting the Concept of Activation in Supercooled Liquids
• Multifractality and statistical localization in highly heterogeneous random networks
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Competition between Barrier- and Entropy-Driven Activation in Glasses
• Bringing together two paradigms of non-equilibrium: Fragile versus robust aging in driven glassy systems
• Random sparse generators of Markovian evolution and their spectral properties
• Non-equilibrium time-dependent solution to discrete choice with social interactions
• Localization properties of the sparse Barrat-Mézard trap model