Universal jamming phase diagram in the hard-sphere limit

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature T, packing fraction phi or pressure p, and applied shear stress Sigma. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities T/p sigma(3), p sigma(3)/epsilon, and Sigma/p, where T is the temperature, p is the pressure, Sigma is the stress, sigma is the sphere diameter, epsilon is the interaction energy scale, and m is the sphere mass. We demonstrate that the phase diagram is universal at low p sigma(3)/epsilon; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are nondimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.