Three-dimensional, three-state Potts model in a negative external field

We investigate the critical behavior of the three-dimensional, three-state Potts model in presence of a negative external field h, i.e. disfavoring one of the three states. A genuine phase transition is present for all values of vertical bar h vertical bar, corresponding to the spontaneous breaking of a residual Z(2) symmetry. The transition is first/second-order, respectively, for small/large values of vertical bar h vertical bar, 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.