Landau theory of glassy dynamics

Abstract

An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering trajectories rapidly diminishes as the ordered ground-state is approached. This leads to an asymmetry in the effective transition rates which results in a non-exponential relaxation of the order-parameter fluctuations and a Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass transition. We argue that the Landau model provides a general framework for studying glassy dynamics in a variety of systems.