  The ABC model is a driven diffusive exclusion model, composed of three
species of particles that hop on a ring with local asymmetric rates. In the
weak asymmetry limit, where the asymmetry vanishes with the length of the
system, the model exhibits a phase transition between a homogenous state and a
phase separated state. We derive the exact solution for the density profiles of
the three species in the hydrodynamic limit for arbitrary average densities.
The solution yields the complete phase diagram of the model and allows the
study of the nature of the first order phase transition found for average
densities that deviate significantly from the equal densities point.
