On the nature of isotherms at first order phase transitions for classical lattice models

Two main results are presented in this paper: Isakov's Theorem about the impossibility of an analytic continuation of the pressure at a first order phase transition point and Friedli's work about the restoration of the analytic continuation of the pressure in the van der Waals limit at such a transition point.An exposition of Pirogov-Sinai theory for models with two periodic ground-states is given in section 3, which can be read independently.