Critical properties of two-level atom systems interacting with a radiation field

The thermodynamic properties of N two-level atoms coupled to radiation field are analyzed taking into account the diamagnetic term by a slight modification to the usual approach to quantizing the electromagnetic field. Following this procedure, we are able to solve the discrepancy originating in the use of different states as a basis for expressing the state of radiation field. We develop a perturbative expansion of partition function and a simple analytic expression is found for a high coupling constant. We show that, in this limit, the interaction of independent atomic spins with a single photon mode can be interpreted as an effective spin-spin interaction of long range nature. Even in this approach, if the diamagnetic term is taken into account, a phase transition at nonzero temperature cannot occur due to sum-rule arguments