Solid-solid transitions induced by repulsive interactions revisited

We revisit a problem already studied 15 years ago by us in collaboration with Stell and Hemmer: the isostructural solid-solid transitions induced by repulsive particle interactions exhibited by classical systems interacting via the Stell-Hemmer potentials. The full phase diagram in the crystal region is obtained by applying a perturbation theory for classical solids used during our collaboration with Stell. Also, the performance of such a theory is now tested by comparing the perturbative phase diagram with that obtained from computer simulations. The latter was calculated using a recently refined method to obtain the free-energy of crystals by means of Monte Carlo simulations. The perturbation theory captures the correct topology and correctly identifies the stable, fcc and bcc, phases. In addition, the theory predicts the occurrence of special points: a point where the two stable structures coexist at the same density, and two critical points terminating the corresponding isostructural phase transitions for fcc and bcc phases. The location of some of these features in the phase diagram is predicted almost quantitatively. However, phase boundaries involving the non-compact bcc phase are much less accurate, a problem that can be traced to the poor representation used for the bcc phase of the reference, hard-sphere, system.