The partition functions of classical systems in the Gaussian equivalent representation of functional integrals

The Gaussian equivalent representation method developed in quantum physics for approximate calculations of functional integrals is applied in the classical statistical physics of liquids to compute the partition and distribution functions for any densities and temperatures. This method works in the case of systems of particles interacting via two-body potentials with the positive Fourier transform. The partition functions for canonical and grand canonical ensembles of classical particles are presented in the form of the Gaussian equivalent representation. The equation of state and the phase transition for the Yukawa potential and the Debye screening for the Coulomb potential are derived.