Statistical description of Coulomb-like systems.

The solution of the problem of the partition function calculation for a Coulomb-like system is proposed. The quantum-field-theory approach is used to give a statistical description of a system of interacting particles with due regard to arbitrary spatially inhomogeneous configurations. Formation of structures in a Coulomb-like system is analyzed and applied to the case of of dusty crystals and two-dimensional colloidal crystals. In the one-dimensional case, an exact solution for the spatial distribution of charged particles is obtained. In the two- dimensional case, the exact partition function for homogeneous distribution of particles is presented. We have analytically derived the necessary condition for the crystal formation in a system of interacting particles in the three-dimensional case.