  The CP-restoring phase transition at theta = pi and high temperature is
investigated using two related models that aim to describe the low-energy
phenomenology of QCD, the NJL model and the linear sigma model coupled to
quarks. Despite many similarities between the models, different predictions for
the order of the phase transition result. Using the Landau-Ginzburg formalism,
the origin of this difference is traced back to a non-analytic vacuum term at
zero temperature that is present in the NJL model, but usually not included in
the linear sigma model. Due to the absence of explicit CP violation, this term
always alters the qualitative aspects of the high temperature phase transition
at theta = pi, just as for theta = 0 in the chiral limit.
