Classical statistics of one-component systems with model potentials

We obtain a functional integral representation of the configuration integra l for one-component classical systems with two-particle potentials admittin g the Fourier expansion. In this representation, the integrand is factored with respect to the atomic coordinates. The "monoatomic" factors are univer sal (i.e., independent of the explicit form of the interatomic potential). We obtain a sufficient condition for spontaneous symmetry breaking in conti nuous classical statistics models. We investigate the case of model potenti als with a nonnegative Fourier transform. The functional integral for this class of potentials is calculated using the saddle-point method. We prove t he existence of phase transitions for some model potentials.