Jamming at zero temperature and zero applied stress: The epitome of disorder

We have studied how two- and three-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 zero applied stress. At low packing fractions φ; the system is not jammed and each particle can move without impediment from its neighbors. For each configuration; there is a unique jamming threshold φ c at which particles can no longer avoid each other; and the bulk and shear moduli simultaneously become nonzero. The distribution of φ c values becomes narrower as the system size increases; so that essentially all configurations jam at the same packing fraction 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 the divergence of the first peak in the pair correlation function and in the vanishing of the pressure; shear modulus; and excess number of overlapping neighbors. 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. Indeed; at point J ; the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity—perhaps even at the glass transition.