Thermodynamics and Superradiant Phase Transitions in a three-level Dicke Model

We analyse the thermodynamic properties of a generalised Dicke model, i.e. a collection of three-level systems interacting with two bosonic modes. We show that at finite temperatures the system undergoes first-order phase transitions only, which is in contrast to the zero-temperature case where a second-order phase transition exist as well. We discuss the free energy and prominent expectation values. The limit of vanishing temperature is discussed as well.