Towards thermal evolution of the most general 2HDM
  We consider the scalar sector of the most general renormalizable two-Higgs-doublet model at non-zero temperature. We calculate the largest finite temperature corrections to the free-energy density and study thermal evolution of the ground state. Within the approximation chosen, we establish all possible sequences of thermal phase transitions and study their relation with the symmetries of the model. We show, in particular, that a charge-breaking or a CP-violating vacuum can arise at intermediate stages of thermal evolution, and that the first-order phase transition is associated with a discrete symmetry of the potential, but not of the entire scalar lagrangian. 
I. P. Ivanov