Tethered Monte Carlo study of the fluid-solid coexistence for hard spheres

We develop an equilibrium numerical approach to crystallization. Focusing on hard-spheres, an effective potential depending on two crystalline order-parameters is computed. Tethered Monte Carlo and its associated Fluctuation Dissipation formalism yields the coexistence pressure for systems with up to 2916 particles. We extrapolate the coexistence pressure to infinite volume, finding $p_\mathrm{co}=11.5727(10) k_\mathrm{B}T/\sigma^3$. At phase coexistence, we study the surface-energy driven geometrical transitions upon varying the order parameters. These transitions occur between bubbles of fluid in a core of crystal (and vice-versa) of spherical, cylindrical and tetragonal shapes.