Phase diagram of Hertzian spheres
  We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of weakly deformable bodies and, therefore, it is a reliable physical model of soft macromolecules, like star polymers and globular micelles. Using thermodynamic integration and extensive Monte Carlo simulations, we computed accurate free energies of the fluid phase and a large number of crystal structures. For this, we defined a general primitive unit cell that allows for the simulation of any lattice. We found multiple re-entrant melting and first-order transitions between crystals with cubic, trigonal, tetragonal, and hexagonal symmetries. 
Josep C. P\`amies, Angelo Cacciuto, Daan Frenkel