Dependence of the glass transition and jamming densities on spatial dimension

Abstract

We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from $d=3$ to $8$, over a wide range of temperatures and densities. Employing a scaling of density-temperature dependent relaxation times, we precisely identify the density ${\varphi }_0$ which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between ${\varphi }_0$ and the athermal jamming density ${\varphi }_J$, small in 3 and 4 dimensions, increases with dimension, with ${\varphi }_0>{\varphi }_J$ for $d>4$. We compare our results with recent theoretical calculations.

Supplemental Material included as ancillary file