Exciton and fermion-pair condensation at non-zero temperature

A thermodynamic study of a many-particle two-level system with the SU(2) circle times SU(2)-symmetry interaction in the particle-particle and particle-hole channels is carried out. Using the symmetry of the system, its free energy and phase diagram are calculated. It is demonstrated that the superconducting (particle-particle) and excitonic (particle-hole) condensates are both formed in the considered system which undergoes two phase transitions. The calculated phase diagram represents qualitatively the phase diagram typical for materials with the high-temperature superconducting properties, including the existence of two phase transitions, the first and second order phase transitions, triple and tricritical points.