Dependence of the glass transition and jamming densities on spatial dimension

TL;DR

This study uses computer simulations across dimensions 3 to 8 to explore how the glass transition and jamming densities depend on spatial dimension, revealing that the difference between these densities grows with dimension.

Contribution

It provides a detailed analysis of the dependence of glass transition and jamming densities on spatial dimension, extending understanding beyond three dimensions.

Findings

The density $oldsymbol{ ho_0}$ for the ideal glass transition is precisely identified.

The difference between $oldsymbol{ ho_0}$ and the jamming density $oldsymbol{ ho_J}$ increases with dimension.

For dimensions greater than 4, $oldsymbol{ ho_0}$ exceeds $oldsymbol{ ho_J}$.

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 $\phi_0$ which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between $\phi_0$ and the athermal jamming density $\phi_J$, small in 3 and 4 dimensions, increases with dimension, with $\phi_0 > \phi_J$ for $d > 4$. We compare our results with recent theoretical calculations.