Clustering in condensed media

A system of classical particles between which there is a Iong-range repulsion and short-range attraction is considered. A method is formulated that makes it possible to find a spatially inhomogeneous distribution of the particles in such a system. The problem is solved in two different physical formulations: 1) the total number of particles in the system is specified, 2) the concentration of a lattice gas is given. For both cases the conditions for the formation of clusters are found. The concentration, size, and critical temperature of their existence are determined. For the second case a cluster equation of state is found.