The high-dimensional fate of hard spheres liquids, glasses, and crystals

Simple liquids and crystals are, to a great extent, well described by the hard sphere model. Yet, while much is known about hard sphere liquids in both high and low dimensions, little is known about their crystal branch for d > 3 or about their liquid branch in intermediate dimensions. This question is particularly important because controlled theoretical developments for dense liquids and glasses are often only accessible in the limit d → ∞. I first consider the the thermodynamic fate of the crystal in high dimensions. Three scenarios are considered: A) crystallization is impeded, making the glass the densest packing; B) crystallization is possible but dynamically prohibited; or C) the crystal phase is thermodynamically accessible from the liquid state. Simulation results in d=3-10 show that the crystal remains thermodynamically stable, and the dimensional trend suggests that scenario C is most likely. Second, I show that the hypernetted chain closure captures both the structure and dynamics of hard sphere liquids and gives a reasonable approximation to the dynamical (mode-coupling) crossover in intermediate dimensions. This identification thus provides a path for relating the high-d liquid branch to actual supercooled liquids.