Connecting real glasses to mean-field models

Abstract

We propose a novel model for a glass-forming liquid, which allows us to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle–particle interactions, which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo-neighbors and by means of analytical calculations, and we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with the increase in k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the mode-coupling theory power law behavior for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with the increase in k, whereas the non-Gaussian parameter is independent of it. Thus, we conclude that with the increase in the number of pseudo-neighbors, the system becomes more mean-field-like. By comparing our results with previous studies on mean-field-like systems, we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit.

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation

“…For all the systems, the data are plotted below their respective onset temperatures (see Table I). 27 The systems follow the expected linear relationship between TSc and T (Fig. 4).…”

“…We find that the excess entropy decreases with increasing k. Our earlier study showed that with increasing k, the structure of the system remains unchanged. 27 Thus, the contribution of the regular neighbors to the entropy does not change with k. However, with an increase in the number of pseudoneighbors and thus U pseudo k , the total excess entropy decreases. Thus, the decrease in excess entropy obtained via the TI method can be attributed to the increase in the pseudoneighbor interactions.…”

“…A similar effect was also seen in the high-temperature dynamics where it was shown that with the increase in the pseudoneighbors, the cage becomes stiffer and the dynamics inside the cage becomes faster. 27 The temperature dependence of the vibrational entropy S vib (obtained from the VDOS) is plotted in Fig. 3.…”

“…In a recent study, some of us have developed a novel generalization of glass-forming liquids where we can switch between a three-dimensional liquid and a fully connected mean-field system in a continuous manner. 27 The parameter that is introduced to achieve this is k added pseudoneighbors for each particle. The structure, dynamics, and dynamical heterogeneity of this model have been studied as a function of k. It was shown that the structure given by the radial distribution function (rdf) of the usual neighbors remains almost unchanged with k. However, the pseudoneighbors do contribute to the total rdf that shows a weaker modulation with distance, a typical mean-field like behavior.…”

“…The structure, dynamics, and dynamical heterogeneity of this model have been studied as a function of k. It was shown that the structure given by the radial distribution function (rdf) of the usual neighbors remains almost unchanged with k. However, the pseudoneighbors do contribute to the total rdf that shows a weaker modulation with distance, a typical mean-field like behavior. 27,28 With an increase in k, the dynamics also slows down and the transition temperatures (T 0 , Tc, Tonset) move to higher values. The range over which a system follows the MCT power-law behavior becomes wider with an increase in k. The heterogeneity decreases with an increase in k. Thus, it was shown that with an increase in k, the system becomes more mean-field like.…”