Journal of Statistical Physics, Vol. 114, Nos. 5/6, March 2004, p. 1235-1267.
We consider extended Pirogov-Sinai models including lattice and continuum particle systems with Kac potentials. Call Lam an intensive variable conjugate to an extensive quantity alpha appearing in the Hamiltonian via the additive term — Lam*аlpha. We suppose that a Pirogov-Sinai phase transition with order parameter а occurs at Lam = 0, and that there are two distinct classes of DLR measures, the plus and the minus DLR measures, with the expectation of alpha respectively positive and negative in the two classes. We then prove that Lam = 0 is the only point in an interval I of values of Lam centered at 0 where this occurs, namely the expected value of a is positive, respectively negative, in all translational invariant DLR measures at ...