  We consider the Potts model on a two-dimensional periodic rectangular lattice
with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the
possible spin values (or colors). The resulting energy landscape is thus
significantly more complex than in the original Ising or Potts models. The
system evolves according to a Glauber-type spin-flipping dynamics. We focus on
a region of the parameter space where there are two symmetric metastable states
and a stable state, and the height of a direct path between the metastable
states is equal to the height of a direct path between any metastable state and
the stable state. We study the metastable transition time in probability and in
expectation, the mixing time of the dynamics and the spectral gap of the system
when the inverse temperature $\beta$ tends to infinity. Then, we identify all
the critical configurations that are visited with high probability during the
metastable transition.
