Dynamics and fluctuations of minimally-structured glass formers

The mean-field theory (MFT) of simple glasses, which is exact in the limit of infinite spatial dimensions, $d\rightarrow\infty$, 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-$d$ corrections 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 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 $\alpha_2$. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations in more realistic glass formers.