  Recent studies have shown that one-dimensional driven systems can exhibit
phase separation even if the dynamics is governed by local rules. The ABC
model, which comprises three particle species that diffuse asymmetrically
around a ring, shows anomalous coarsening into a phase separated steady state.
In the limiting case in which the dynamics is symmetric and the parameter $q$
describing the asymmetry tends to one, no phase separation occurs and the
steady state of the system is disordered. In the present work we consider the
weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and
study how the disordered state is approached. In the case of equal densities,
we find that the system exhibits a second order phase transition at some
nonzero $\beta_c$.
  The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be
obtained by writing the exact large deviation functional. For nonequal
densities, we write down mean field equations and analyze some of their
predictions.
