On the stability of a quasicrystal and its crystalline approximant in a system of hard disks with a soft corona

Using computer simulations, we study the phase behavior of a model system of colloidal hard disks
with a diameter σ and a soft corona of width 1.4σ. The particles interact with a hard core and a
repulsive square-shoulder potential. We calculate the free energy of the random-tiling quasicrystal and
its crystalline approximants using the Frenkel-Ladd method. We explicitly account for the configurational
entropy associated with the number of distinct configurations of the random-tiling quasicrystal.
We map out the phase diagram and find that the random tiling dodecagonal quasicrystal is stabilised
by entropy at finite temperatures with respect to the crystalline approximants that we considered, and
its stability region seems to extend to zero temperature as the energies of the defect-free quasicrystal
and the crystalline approximants are equal within our statistical accuracy.