Stability of Gibbs distributions

Lattice systems with binary interaction are considered. The Gibbs distributions characterizing the states of the systems are determined by generating functionals that satisfy Bogolyubov's equation. It is shown that to different regularity conditions of the Gibbs distributions there correspond different natures of the continuous dependence of the solutions of the Bogolyubov equation on the external field. This makes it possible to regard the regularity conditions as conditions of stability of the Gibbs distributions with respect to weak perturbations of them by external fields.