Models of traps and glass phenomenology

TL;DR

This paper investigates models of particles hopping between energy traps, revealing phase transitions, aging effects, and relaxation behaviors, with extensions to interacting particles and energy-dependent diffusion.

Contribution

It introduces a comprehensive analysis of trap models with various energy distributions, highlighting phase transitions, aging phenomena, and effects of interactions.

Findings

Exponential trap energy distributions cause a phase transition between liquid and aging phases.

Relaxation functions show characteristic shoulders fitted by stretched exponentials.

Interacting particles modify diffusion dynamics and relaxation properties.

Abstract

We study various models of independent particles hopping between energy `traps' with a density of energy barriers $\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\rho(E)$ decays exponentially, a true dynamical phase transition between a high temperature `liquid' phase and a low temperature `aging' phase occurs. More generally, however, one expects that for a large class of $\rho(E)$, `interrupted' aging effects appear at low enough temperatures, with an ergodic time growing faster than exponentially. The relaxation functions exhibit a characteristic shoulder, which can be fitted as stretched exponentials. A simple way of introducing interactions between the particles leads to a modified model with an effective diffusion constant in energy space, which we discuss in detail.