Abstract
We consider extended Pirogov–Sinai models including lattice and continuum particle systems with Kac potentials. Call λ an intensive variable conjugate to an extensive quantity α appearing in the Hamiltonian via the additive term −λα. We suppose that a Pirogov–Sinai phase transition with order parameter α occurs at λ=0, and that there are two distinct classes of DLR measures, the plus and the minus DLR measures, with the expectation of α respectively positive and negative in the two classes. We then prove that λ=0 is the only point in an interval I of values of λ centered at 0 where this occurs, namely the expected value of α is positive, respectively negative, in all translational invariant DLR measures at {λ>0}⊓I and {λ<0}⊓I.
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Bovier, A., Merola, I., Presutti, E. et al. On the Gibbs Phase Rule in the Pirogov–Sinai Regime. Journal of Statistical Physics 114, 1235–1267 (2004). https://doi.org/10.1023/B:JOSS.0000013970.66907.b9
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DOI: https://doi.org/10.1023/B:JOSS.0000013970.66907.b9