Parity-violating electromagnetic interactions in QED_3 at finite   temperature
  We study the parity-breaking terms generated by the box diagram in 2+1 dimensional thermal QED. These lead, in the long wave limit, to a gauge invariant extensive action which behaves as 1/T at high temperature. In contrast, the effective action in the static limit involves leading non-extensive terms proportional to 1/T^3 at high temperature, which violate large gauge invariance. We derive a non-linear large gauge Ward identity, which relates the leading static terms of different order in perturbation theory and whose solution coincides with the all order effective action proposed earlier. 
F. T. Brandt, Ashok Das and J. Frenkel