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Description
The thermodynamic properties of a system of interacting relativistic bosonic particles and antiparticles at high temperatures and densities, in the presence of the Bose-Einstein condensate, are studied. The density functional mean-field model and the scalar field model were used to calculate phase diagrams and thermodynamic quantities for different ratios of attractive to repulsive forces in the system. As an example, a system of interacting pions ($\pi^{\pm}$) was considered. It is shown that, depending on the interaction constant, four types of phase transitions to the condensate phase exist in such a system. Three are second-order phase transitions, and one is a first-order phase transition. Model calculations were compared with up-to-date lattice data, and parameters were fitted accordingly.