Summary: A continuous infinite system of point particles interacting via infinite range many-body potentials of superstable type is considered in the framework of the classical statistical mechanics. We propose a very transparent prove of the uniform bounds for a family of finite volume correlation functions. This gives the possibility to prove that for any temperature and chemical activity there exists at least one Gibbs state. This article is a generalization of a paper of O. V. Kutoviy and A. L. Rebenko [J. Math. Phys. 45, No. 4, 1593–1605 (2004; Zbl 1068.82008)] for the case of infinite range interaction potentials.
For part I, cf. Methods Funct. Anal. Topol. 13, No. 1, 50–61 (2007; Zbl 1150.82001).