On the Gibbs phase rule in the Pirogov-Sinai regime

We consider extended Pirogov - Sinai models including lattice and continuum particle systems with Kac potentials. Call lambda an intensive variable conjugate to an extensive quantity alpha appearing in the Hamiltonian via the additive term - lambdaalpha. We suppose that a Pirogov - Sinai phase transition with order parameter alpha occurs at lambda = 0, and that there are two distinct classes of DLR measures, the plus and the minus DLR measures, with the expectation of a respectively positive and negative in the two classes. We then prove that lambda = 0 is the only point in an interval I of values of lambda centered at 0 where this occurs, namely the expected value of alpha is positive, respectively negative, in all translational invariant DLR measures at {lambda > 0} I and {lambda < 0} I.