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

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.