Dynamical criticality in high-dimensional glass-forming liquids.*

The mean-field theory of glass formation predicts the existence of a dynamical critical point at which the relaxation time diverges. Due to the presence of activated processes in physical dimensions (d=2, 3), this critical point is then but a crossover. Some of the associated phenomenology is nonetheless considered to persist. We here aim to identify what, if anything, of this criticality can be clearly identified by systematically varying the dimension of space. Using fluids of polydispersed hard spheres that have been optimized for the swap Monte Carlo algorithm allows us to thermalize very high-density systems and thus to approach the regime of interest easily. We then examine markers of dynamical criticality, such as the fluctuations of dynamical correlators and dynamical heterogeneity.