Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

TL;DR

This study investigates the jamming transition in disordered particle systems at zero temperature and stress, revealing critical-like behavior at the random close-packing density, with implications for understanding glassy states.

Contribution

It provides a detailed characterization of the jamming transition at Point J, defining its properties and critical behavior in terms of packing fraction and interparticle potentials.

Findings

Jamming occurs at a well-defined density corresponding to random close-packing.

Near Point J, many quantities exhibit power-law scaling and diverging length scales.

The vibrational density of states shows an excess of low-frequency modes approaching Point J.

Abstract

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.