  We investigate the critical behaviour of the three-dimensional, three state
Potts model in presence of a negative external field h, i.e. disfavouring one
of the three states. A genuine phase transition is present for all values of
|h|, corresponding to the spontaneous breaking of a residual Z_2 symmetry. The
transition is first/second order respectively for small/large values of |h|,
with a tricritical field h_tric separating the two regimes. We provide, using
different and consistent approaches, a precise determination of h_tric; we also
compare with previous studies and discuss the relevance of our investigation to
analogous studies of the QCD phase diagram in presence of an imaginary chemical
potential.
