Magnetic Catalysis of Chiral Symmetry Breaking in QED at Finite Temperature

The catalysis of chiral symmetry breaking by a magnetic field in the massless weak-coupling phase of QED is studied. The dynamical mass of a fermion (energy gap in the fermion spectrum) is shown to depend essentially nonanalytically on the renormalized coupling constant $\alpha$ in a strong magnetic field. The temperature of the symmetry restoration is calculated analytically as $T_c\approx m_{dyn}$, where $m_{dyn}$ is the dynamical mass of a fermion at zero temperature.