Landau theory of glassy dynamics

TL;DR

This paper presents an exact Landau model solution illustrating how a funnel-shaped energy landscape causes glassy dynamics, including non-exponential relaxation and divergence of relaxation times, offering a general framework for glass transition studies.

Contribution

It introduces an exact Landau model capturing glassy dynamics with activated critical behavior and a funnel-shaped energy landscape, advancing theoretical understanding.

Findings

Non-exponential relaxation of order-parameter fluctuations

Vogel-Fulcher-Tammann divergence of relaxation times

Model describes glass transition phenomena

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.