Dynamics and fluctuations of minimally structured glass formers

The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, d→∞, offers theoretical insight as well as quantitative predictions about certain features of $d=3$ systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as d increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter α₂. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.