Hamiltonian of the phase separation border and phase transitions of the first kind. I

The Pirogov–Sinai theory of phase transitions of the first kind is generalized to the case when the “ground states” of the Hamiltonian of the model are interacting random fields (disordered phases). Border Hamiltonians and corresponding Ursell functions are introduced, and also conditions on them (cluster estimates) that ensure the existence of phase transitions, analyticity of the thermodynamic and correlation functions in the region of stability of given phases, analyticity of the strata of the phase diagram, and convergence of the constructed cluster expansions.