On the Free Energy of Noncommutative Quantum Electrodynamics at High Temperature

TL;DR

This paper calculates the free energy of noncommutative QED at high temperature, including higher-order loop corrections, revealing a non-perturbative behavior and potential phase transition due to thermodynamic instability.

Contribution

It provides the first detailed analysis of the free energy in noncommutative QED at high temperature, incorporating three-loop contributions and ring diagrams, highlighting non-analytic effects and phase transition indications.

Findings

Non-perturbative e^3 behavior at high temperature

Thermodynamic instability above a critical temperature

Potential phase transition in noncommutative QED

Abstract

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 {\it ring diagrams} and obtain a result which has a peculiar dependence on the coupling constant. For large values of $e\theta T^2$ ($\theta$ is the magnitude of the noncommutative parameters) this non-perturbative contribution exhibits a non-analytic behavior proportional to $e^3$. We show that above a certain critical temperature, there occurs a thermodynamic instability which may indicate a phase transition.