Random First Order Phase Transition Theory of the Structural Glass Transition

TL;DR

This paper presents a theory of the structural glass transition based on a random first order phase transition, explaining the dynamics, thermodynamics, and heterogeneity of glasses through metastable states and a mean-field approach.

Contribution

It introduces a static and dynamic theory of the glass transition using a density functional and mean-field framework, highlighting the role of metastable states and the violation of the law of large numbers.

Findings

Existence of exponentially many metastable states below $T_A$

Non-extensive number of glassy states below $T_K$

Link between dynamic heterogeneity and violation of law of large numbers

Abstract

We describe our perspective on the Structural Glass Transition (SGT) problem built on the premise that a viable theory must provide a consistent picture of the dynamics and statics, which are manifested by large increase in shear viscosity and thermodynamic anamolies respectively. For the static and dynamic description to be consistent we discovered, using a density functional description without explicit inclusion of quenched random interactions and a mean-field theory, that there be an exponentially large number of metastable states at temperatures less than a critical transition temperature, $T_A$. At a lower temperature ($T_K < T_A$), which can be associated with the Kauzmann temperature, the number of glassy states is non-extensive. Based on this theory we formulated an entropic droplet picture to describe transport in finite dimensions in the temperature range $T_K < T < T_A$. From the finding that glasses are trapped in one of many metastable states below $T_A$ we argue that during the SGT law of large numbers is violated. As a consequence in glasses there are sub sample to sub sample fluctuations provided the system is observed for times longer than the typical relaxation time in a liquid. These considerations, which find support in computer simulations and experiments, also link the notion of dynamic heterogeneity to the violation of law of large numbers. Thus, the finding that there is an extensive number of metastable states in the range $T_K < T < T_A$ offers a coherent explanation of many of the universal features of glass forming materials.