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Using the general structure of the vacuum polarization tensor$\Pi_{\mu\nu}(k_{0},\mathbf{k})$ in the infrared (IR) limit, $k_{0}\to 0$, thering contribution to QED effective potential at finite temperature and non-zeromagnetic field is determined beyond the static limit, $(k_{0}\to0,\mathbf{k}\to \mathbf{0})$. The resulting ring potential is then studied inweak and strong magnetic field limit. In the limit of weak magnetic field, athigh temperature and for $\alpha\to 0$, the improved ring potential consists ofa term proportional to $T^{4}\alpha^{5/2}$, in addition to the expected$T^{4}\alpha^{3/2}$ term arising from the static limit. Here, $\alpha$ is thefine structure constant. In the limit of strong magnetic field, where QEDdynamics is dominated by the lowest Landau level (LLL), the ring potentialincludes a novel term consisting of dilogarithmic function$(eB){Li}_{2}(-\frac{2\alpha}{\pi}\frac{eB}{m^{2}})$. Using the ring improved(one-loop) effective potential including the one-loop effective potential andring potential in the IR limit, the dynamical chiral symmetry breaking of QEDis studied at finite temperature and in the presence of strong magnetic field.The gap equation, the dynamical mass and the critical temperature of QED in theregime of LLL dominance are determined in the improved IR as well as in thestatic limit. For a given value of magnetic field, the improved ring potentialis shown to be more efficient in decreasing the critical temperature arisingfrom one-loop effective potential.

Improved ring potential of QED at finite temperature and in the presence of weak and strong magnetic field