Models of traps and glass phenomenology

Cecile Monthus 1, 2, Jean-Philippe Bouchaud 3

Journal of Physics A 29 (1996) 3847-3869

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.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud
  • 3. Service de physique de l'état condensé (SPEC),
    CNRS : URA2464 – CEA : DSM/IRAMIS