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. Calling λ an intensive variable conjugate to an extensive quantity α appearing in the Hamiltonian via the additive term −λα, we prove that if a Pirogov-Sinai phase transition with order parameter α occurs at λ = 0, then this is the only point in an interval of values of λ centered at 0, where phase transitions occur.