Interphase Hamiltonian and first-order phase transitions: A generalization of the Lee–Yang theorem

We generalize the Pirogov–Sinai theory and prove the results applicable to first-order phase transitions in the case of both bulk and surface phase lattice models. The region of first-order phase transitions is extended with respect to the chemical activities to the entire complex space $\mathbb C^\Phi$, where $\Phi$ is the set of phases in the model. We prove a generalization of the Lee–Yang theorem: as functions of the activities, the partition functions with a stable boundary condition have no zeros in $\mathbb C^\Phi$.