Model for dynamics of structural glasses

Abstract

We have studied, using dynamical Monte Carlo methods, a facilitated kinetic Ising model for structural glasses. We observe stretched-exponential decays (␣ relaxation͒ of the equilibrium spin autocorrelation function at late times and are able to estimate accurately the corresponding relaxation times . These are found to diverge at nonzero temperatures following a Vogel-Fulcher law. In addition, we observe early-time exponential relaxation analogous to ␤ relaxation of glass formers. We also examined the effective thermodynamics of systems quenched below this divergent temperature and subsequently heated. The result is a peak in the specific heat with properties matching those of the putative glass transition. We also find that these peaks, for different heating rates, can be rescaled to lie on a universal curve. Finally, we studied the evolving structure factor of a frozen glass following a rapid jump in temperature. The results are qualitatively the same as those for x-ray studies of heated glasses. We thus demonstrate that this purely dynamical microscopic model can reproduce much of the phenomenology of the glass transition and near-glass relaxation, with no tunable parameters. ͓S1063-651X͑97͒07301-7͔

Out-of-equilibrium dynamical fluctuations in glassy systems

“…A crossover ͑in the total time͒ between the ''easy'' initial regime and the ''hard'' latter regime was predicted in Ref. 43.…”

“…52 This value is considerably lower than the putative glass transition identified by Graham, Piché, and Grant. 43 These authors might have overestimated this temperature by simulating very small systems ͑of maximum size Vϭ16 3 ) as compared to the ones we use (Vϭ128 3 ).…”

“…It is a simple variation of the Fredrickson-Andersen ͑FA͒ model 28 due to Graham, Piché, and Grant. 43 Thus there are no static interactions between the spins but an external field of strength h is applied. The system is in contact with a heat bath at temperature T that, for convenience, we shall measure in units of the external field h. This model does not have a static transition and at equilibrium the aver-…”

“…In Sec. IV we introduce the models that we study numerically; these are a modification of the Fredrickson-Andersen ͑FA͒ model due to Graham, Piché, and Grant 43 and the Edwards-Anderson ͑EA͒ spin glass. 44 In Sec.…”

Connecting microscopic simulations with kinetically constrained models of glasses

“…An alternative approach to reach low temperatures and long times, but without a microscopic foundation, is to study simple models of glassiness, kinetically constrained models (KCMs) [19,20,21,22,23,24], such as the Fredrickson-Andersen (FA) model [20] or the East model [25], or variations such as the North-East model [23], which mimic the constrained dynamics of real glassy systems but have trivial thermodynamics. These may be viewed as effective models for glasses, in terms of some coarse-grained degree of freedom often labelled "spins", also termed a "mobility field" by some authors [23].…”