Stability of the tree-level vacuum in two Higgs doublet models against   charge or CP spontaneous violation
  We show that in two Higgs doublet models at tree-level the potential minimum preserving electric charge and CP symmetries, when it exists, is the global one. Furthermore, we derived a very simple condition, involving only the coefficients of the quartic terms of the potential, that guarantees spontaneous CP breaking. 
P.M. Ferreira, R. Santos, A. Barroso