Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder p lane of a hard-sphere system in the presence of quenched, random, pinning d isorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stabilit y is studied as a function of the density and the strength of disorder. Reg ions in the phase diagram corresponding to liquid, glassy, and nearly cryst alline states are mapped out, and the nature of the transitions is determin ed. The liquid to glass transition changes from first to second order as th e strength of the disorder is increased. For weak disorder, the system unde rgoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is repla ced by a continuous glass transition. Our numerical results are compared wi th those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are dis cussed.