Connecting real glasses to mean-field models
Résumé
We propose a novel model for a glass-forming liquid which allows 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 neighbours and by means of analytical calculations, we determine the
structural properties related to these additional neighbors. We show that the relaxation dynamics of the
system slows down very quickly with increasing k and that the onset and the mode-coupling temperatures
increase. The systems with high values of k follow the MCT power law behaviour for a larger temperature
range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic
heterogeneity decreases with increasing k whereas the non-Gaussian parameter is independent of it. Thus we
conclude that with the increase in the number of pseudo neighbours the system becomes more mean-field like.
By comparing our results with previous studies on mean-field like system 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.
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