Three-dimensional QED at finite temperature

We investigate the finite temperature behaviour of (2+1)-dimensional QED with N flavours of fermions. The Landau gauge photon propagator is calculated to leading order in the large-N expansion at zero frequency. As in four-dimensional gauge theories the temporal component of the photon acquires a mass at non-zero temperature and static external electric fields are screened. We study the effect of thermal screening on dynamical fermion mass generation using an approximate treatment of the Schwinger-Dyson equation for the fermion self-energy. Numerical results for the temperature dependence of the dynamically generated fermion mass are presented for a range of values of the gauge coupling and of N. We find a non-zero critical temperature above which the fermion mass vanishes identically. In particular, we find that the ratio of the zero-temperature fermion mass to the critical temperature is approximately independent of N and is large compared to four-fermion theories. (orig.)