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We consider the computation of the coexistence pressure of the liquid-solid transition of a systemof hard spheres from direct simulation of the inhomogeneous system formed from liquid and solidphases separated by an interface. Monte Carlo simulations of the interfacial system are performedin three different ensembles. In a first approach, a series of simulations is carried out in theisothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystallinestructure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of thesystem fluctuates due to changes in the three dimensions of the simulation box. In a secondapproach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemblewhere the normal pressure, as well as the area of the  planar  fluid-solid interface, are kept constant.Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of thesimulation box. In both approaches, the coexistence pressure is estimated by monitoring theevolution of the density along several simulations carried out at different pressures. Both routes areseen to provide consistent values of the fluid-solid coexistence pressure, p=11.54 4 kBT/ 3, whichindicates that the error introduced by the use of the standard constant-pressure ensemble for thisparticular problem is small, provided the systems are sufficiently large. An additional simulation ofthe interfacial system is conducted in a canonical ensemble where the dimensions of the simulationbox are allowed to change subject to the constraint that the total volume is kept fixed. In thisapproach, the coexistence pressure corresponds to the normal component of the pressure tensor,which can be computed as an appropriate ensemble average in a single simulation. This route yieldsa value of p=11.54 4 kBT/ 3. We conclude that the results obtained for the coexistence pressurefrom direct simulations of the liquid and solid phases in coexistence using different ensembles aremutually consistent and are in excellent agreement with the values obtained from free energycalculations

Determination of the melting point of hard spheres from direct coexistence simulation methods