Resummation of diagram expansions in polarized systems with charged particles

Classical equilibrium system including charged and neutral particles is considered. By means of splitting the interaction potential into the short-range and long-range electrostatic parts, the diagram expansions with respect to electrostatic interaction due to the presence of the charge of particles and induced as well as rigid dipoles are constructed. A procedure of the resummation of the initial expansions is suggested which means essentially the transition to irreducible diagrams and removes completely the long-range divergencies due to the slow decreasing of the electrostatic interaction as well as the short-distance divergencies. With the help of taking explicitly into account the dipole interaction one obtains the usual renormalization of the Coulomb interaction by means of the dielectric constant $\varepsilon$. Polarisation corrections in higher approximations are found which cannot he described by means of the direct introducing of the constant $\varepsilon$ into the Coulomb interaction potential.