  While the glass transition at non-zero temperature seems to be hard to access
for experimental, theoretical, or simulation studies, jamming at zero
temperature has been explored in great detail. It is a widely discussed
question whether this athermal jamming transition is related to the glass
transition. Motivated by the exploration of the energy landscape that has been
successfully used to describe athermal jamming, we introduce a new method to
determine whether the configuration space of a soft sphere system can be
explored within a reasonable timescale or not, i.e., whether the system is
ergodic or effectively non-ergodic. While in case of athermal jamming for a
given random starting configuration only the local energy minimum is
determined, we allow the thermally excited crossing of energy barriers.
Interestingly, we observe that a transition exists where the system becomes
effectively non-ergodic if the density is increased. In the limit of small but
non-zero temperatures the density where the ergodicity breaking transition
occurs approaches a value that is independent of temperature and below the
transition density of athermal jamming. This confirms recent computer
simulation studies where athermal jamming occurs deep inside the glass phase.
In addition, with our method we determined the critical behavior of the
ergodicity breaking transition and show that it is in the universality class of
directed percolation. Therefore, our approach not only makes the transition
from an ergodic to an effectively non-ergodic systems easily accessible and
helps to reveal its universality class but also shows that it is fundamentally
different from athermal jamming.
