  We study the nature of the glass transition by cooling model atomistic glass
formers at constant rate from a temperature above the onset of glassy dynamics
to $T=0$. Motivated by the East model, a kinetically constrained lattice model
with hierarchical relaxation, we make several predictions about the behavior of
the supercooled liquid as it passes through the glass transition. We then
compare those predictions to the results of our atomistic simulations.
Consistent with our predictions, our results show that the relaxation time
$\tau$ of the material undergoes a crossover from super-Arrhenius to Arrhenius
behavior at a cooling-rate-dependent glass transition temperature $T_\text{g}$.
The slope of $\ln\tau$ with respect to inverse temperature exhibits a peak near
$T_\text{g}$ that grows more pronounced with slower cooling, matching our
expectations qualitatively. Additionally, the limiting value of this slope at
low temperature shows remarkable quantitative agreement with our predictions.
Our results also show that the rate of short-time particle displacements
deviates from the equilibrium linear scaling around $T_\text{g}$,
asymptotically approaching a different linear scaling. To our surprise, these
short-time displacements, the dynamic indicators of the underlying excitations
responsible for structural relaxation, show no spatial correlations beyond a
few particle diameters, both above and below $T_\text{g}$. This final result is
contrary to our expectation, based on previous results for East model glasses
formed by cooling, that inter-excitation correlations should emerge as the
liquid vitrifies.
