Freezing and clustering transitions for penetrable spheres

We consider a system of spherical particles interacting by means of a pair potential equal to a finite constant for interparticle distances smaller than the sphere diameter and zero outside. The model may be a prototype for the interaction between micelles in a solvent [C. Marquest and T. A. Witten, J. Phys. France 50, 1267 (1989)]. The phase diagram of these penetrable spheres is investigated using a combination of cell- and density functional theory for the solid phase together with simulations for the fluid phase. The system displays unusual phase behavior due to the fact that, in the solid, the optimal configuration is achieved when certain fractions of lattice sites are occupied by more than one particle, a property that we call `clustering'. We find that freezing from the fluid is followed, by increasing density, by a cascade of second-order, clustering transitions in the crystal.