Statistical description of model systems of interacting particles and phase transitions accompanied by cluster formation

Abstract

We develop an approach to the statistical description of a system of interacting particles in order to describe spatially inhomogeneous structures. A criterion is proposed for selecting system states whose contributions in the partition function are dominant. A nonperturbative calculation of the partition function is demonstrated. The known results for various systems (hard sphere model, gravitating gas, etc.) are reproduced. Spatially inhomogeneous system states are considered. The conditions for the phase transition accompanied with cluster formation are found for model systems. Cluster size distribution and cluster interaction residual energy are estimated. The formation of new spatial structures in a cluster system is considered.