  Numerical simulations of systems at coexistence are known to yield unstable
fields in some regions of the density parameters, as well as inequivalence of
ensembles. The Van der Waals-like loops are attributed to effects of the
interface between the coexisting phases, but the question of convexity remains
unresolved. We recover the theory developed by Hill in the 1960's, and adapt it
to include the interface free energy. Our adapted theory is verified through
carefully planned simulations, and gives a thermodynamic description of the
interface behaviour inside the coexistence region which restores the proper
convexity of the thermodynamic potentials, as well as yields convergence of
grandcanonical and canonical results. As a bonus, our interpretation allows
direct calculation of surface tension in very good accordance with Onsager's
analytic prediction.
