Geometry of the equilibrium distribution of interacting particles

The formations of structures in all systems of interacting particles at different temperatures and particle concentrations have the same physical nature and therefore they could be described geometrically the same way. We propose a geometric description of a thermodynamically stable distribution of interacting particles. The character and intensity of interaction between particles determine the effective geometry of the medium which is provided by the minimum of the total free energy with non-linearity. A realization of spaces with possible particle distributions of arbitrary-order symmetries (including fifth, seventh etc. orders) which cannot occur in the ordinary Euclidean space, is described.