Dynamics and effective thermodynamics of a model structural glass

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Abstract
We use Monte Carlo methods to investigale a purely dynamical madel for structural glasses. We observe stretched exponential decays of the equilibrium autocomhlion function and measure the late-time relaxalion limes r. These diverge with temperature following a Vogel- Fulcher law. We also study systems which are quenched deeply and then re-heated. This gives a peak in the effective specific heat with pmpenies matching those of the glass transitiok ?he model thus reproduces the main phenomenology of glasses and the glass transition. It is thought that structural glasses are not equilibrium phases but are materials trapped in long-lived metastable states. However, the mechanism by which this trapping occurs is not known, as is how its onset near a glass can give rise to non-exponential decays of autocordation functions, and to a divergence in the relaxation time at a non-zero temperature. In addition it is not obvious how such a purely dynamical outlook can yield the first-order-like thermal properties of the glass transition. Given these difficulties much effort has been devoted to developing a well-defined dynamical model which reproduces these phenomena. In this Letter we present a purely dynamical model for smctural glasses that tests the idea of local frustration as the relevant microscopic mechanism. This is a simplified version of the facilitated kinetic Ising model of Fredrickson and Andersen (FA) (?,?I. Here we reconsider this idea in both two and three dimensions, generating results with improved statistics and examining the effective thermodynamics upon heating and cooling. At low temperatures the equilibrium autocorrelation functions have the late-time stretched exponential decays characteristic of glass-forming materials. More importantly we can use these data to measure the late-time temperaturedependent relaxation times 5. In all cases that our data are best represented by a r which diverges at a non-zero temperature following a Vogel-Fulcher (VF) law. Lastly, our simulations of heating and cooling of a quenched low- temperature 'glass' show a peak in the effective specific heat with properties very similar to those of experimental glass transitions. Thus this model is able to reproduce much of the phenomenology of glassy relaxation and the glass transition, with no adjustable parameters. We emphasize that our model is an extremely simple spin model for the glass transition, with built-in dynamic frustration. As such, it differs fundamentally from molecular models for structural glasses (which can be based on, for example, the detailed molecular interactions in a binary alloy). Nevertheless. the present model leads to long-time behaviour which bears similarities with the more realistic models, thereby suggesting that the long- time features of stretched exponential decay and a VF law may be intrinsically dynamical phenomena.

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