Abstract
The thermodynamic properties of a system of interacting boson particles and antiparticles at finite temperatures are studied within the framework of the thermodynamically consistent Skyrme-like mean-field model. The mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. We assume a conservation of the isospin density for all temperatures. It is shown that, independently of the strength of the attractive mean field, at the critical temperature ${T}_{\mathrm{c}}$ the system undergoes the phase transition of second order to the Bose-Einstein condensate, which exists in the temperature interval $0\ensuremath{\le}T\ensuremath{\le}{T}_{\mathrm{c}}$. We obtained that the condensation represents a discontinuity of the derivative of the heat capacity at $T={T}_{\mathrm{c}}$, and condensate occurs only for the component with a higher particle-number density in the particle-antiparticle system.
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