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

TY - JOUR

T1 - From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks

AU - Tapias, Diego

AU - Paprotzki, Eva

AU - Sollich, Peter

PY - 2020/9/23

Y1 - 2020/9/23

N2 - 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 (RRG). 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.

AB - 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 (RRG). 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.

KW - Ageing

KW - Cavity and replica method

KW - Energy landscapes

KW - Glassy dynamics

KW - Slow relaxation

UR - http://www.scopus.com/inward/record.url?scp=85092582428&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/abaecf

DO - 10.1088/1742-5468/abaecf

M3 - Article

SN - 1742-5468

VL - 2020

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 9

M1 - 093302

ER -