Coexistence point in the six-vertex model and the crystal shape of fcc materials

By numerical and analytic study of the exact solution to the six-vertex model in applied fields, we explore in detail an unusual coexistence point which occurs in the low-temperature ferroelectric regime. This point, whose existence had been previously conjectured, corresponds to additional singularities in the free energy which were overlooked in the discussion of the original solution of the model. Furthermore, we find interesting scaling properties in the vicinity of this point. Implications for crystal shapes and the phase separation of unstable crystal surfaces are also discussed.