Classical statistics of one-component systems with model potentials

We obtain a functional integral representation on the configuration integral for one-component classical systems with two-particle potentials admitting the Fourier expansion. In this representation, the integrand is factored with respect to the atomic coordinates. The “monoatomic” factors are universal (i.e., independent of the explicit form of the interatomic potential). We obtain a sufficient condition for spontaneous symmetry breaking in continuous classical statistics models. We investigate the case of model potentials with a nonnegative Fourier transform. The functional integral for this class of potentials is calculated using the saddle-point method. We prove the existence of phase transitions for some model potentials.