On the free energy of noncommutative quantum electrodynamics at high temperature

We compute higher order contributions to the free energy of noncommutative quantum electrodynamics at a nonzero temperature T. Our calculation includes up to three-loop contributions (fourth order in the coupling constant e). In the high temperature limit we sum all the ring diagrams and obtain a result which has a peculiar dependence on the coupling constant. For large values of eθT2 (θ is the magnitude of the noncommutative parameters) this nonperturbative contribution exhibits a nonanalytic behavior proportional to e3. We show that above a certain critical temperature, there occurs a thermodynamic instability which may indicate a phase transition.