Four types of phase transitions in interacting boson (meson) matter at high temperatures

The thermodynamics of the interacting system of relativistic particles and antiparticles in the presence of a Bose-Einstein condensate was investigated within the framework of the mean-field model. It is assumed that the total isospin (charge) density is conserved. We show that, depending on the strength of the interaction, a bosonic particle-antiparticle system exhibits four types of phase transitions to the condensate phase. Three types correspond to the second-order phase transition, while one is a first-order phase transition.