Abstract
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 studied in great detail. Motivated by the exploration of the energy landscape that has been successfully used to investigate athermal jamming, we introduce a new method that includes the possibility of the thermally excited crossing of energy barriers. We then determine whether the ground state configurations of a soft sphere system are accessible or not and as a consequence whether the system is ergodic or effectively non-ergodic. Interestingly, we find an transition where the system becomes effectively non-ergodic if the density is increased. The transition density in the limit of small but non-zero temperatures 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, we show that the ergodicity breaking transition 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.
Highlights
When increasing the density or decreasing the temperature many particulate systems reach a state where no longer any significant dynamics can be observed such that the system is in an amorphous, effectively solid state
Depending on the packing fraction of the system, either all overlaps have been removed, which corresponds to a ground state and is called an unjammed system, or the configuration at the local minimum contains overlapping particles, which is called a jammed configuration
Our new method for p = 0, i.e., without any crossing of energy barriers, leads to the well-known athermal jamming transition at a packing fraction of φJ = 0.638 which is in agreement with the results for a monodisperse system reported in[18,19]
Summary
When increasing the density or decreasing the temperature many particulate systems reach a state where no longer any significant dynamics can be observed such that the system is in an amorphous, effectively solid state. Depending on the packing fraction of the system, either all overlaps have been removed, which corresponds to a ground state and is called an unjammed system, or the configuration at the local minimum contains overlapping particles, which is called a jammed configuration. Note that such a jammed configuration obviously is not a ground state and that as a consequence jammed systems usually are not in equilibrium, because in principle ground states might still exist but are just not accessed. Simulations[26,27,28,29,30] suggests that the athermal jamming transition might occur inside the glass phase at small but nonzero temperatures
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