Ising Model of a Glass Transition

TL;DR

This paper models the glass transition using an Ising-like framework, explaining diverging correlation lengths and relaxation times in glass-forming systems through a two-state cluster approach, supported by statistical thermodynamics and simulation data.

Contribution

It introduces an Ising-like model for glass transition based on locally ordered clusters, providing a theoretical explanation consistent with simulation results.

Findings

The model accurately fits simulation data.

Correlation lengths diverge near the glass transition.

The theory links Ising-like behavior with Vogel-Fulcher-Tamann relaxation.

Abstract

Numerical simulations by Tanaka and coworkers indicate that glass forming systems of moderately polydisperse hard-core particles, in both two and three dimensions, exhibit diverging correlation lengths. These correlations are described by Ising-like critical exponents, and are associated with diverging, Vogel-Fulcher-Tamann, structural relaxation times. Related simulations of thermalized hard disks indicate that the curves of pressure versus packing fraction for different polydispersities exhibit a sequence of transition points, starting with a liquid-hexatic transition for the monodisperse case, and crossing over with increasing polydispersity to glassy, Ising-like critical points. I propose to explain these observations by assuming that glass-forming fluids contain twofold degenerate, locally ordered clusters of particles, similar to the two-state systems that have been invoked to explain other glassy phenomena. This paper starts with a brief statistical derivation of the thermodynamics of thermalized, hard-core particles. It then discusses how a two-state, Ising-like model can be described within that framework in terms of a small number of statistically relevant, internal state variables. The resulting theory agrees accurately with the simulation data. I also propose a rationale for the observed relation between the Ising-like correlation lengths and the Vogel-Fulcher-Tamann formula.