Superstable interactions in classical statistical mechanics

We consider classical systems of particles inv dimensions. For a very large class of pair potentials (superstable lower regular potentials) it is shown that the correlation functions have bounds of the form $$\varrho (x_1 ,...,x_n ) \leqq \xi ^n$$ . Using these and further inequalities one can extend various results obtained by Dobrushin and Minlos 3] for the case of potentials which are non-integrably divergent at the origin. In particular it is shown that the pressure is a continuous function of the density. Infinite system equilibrium states are also defined and studied by analogy with the work of Dobrushin 2a] and of Lanford and Ruelle 11] for lattice gases.