Parity-breaking electromagnetic interactions in thermal QED_3
  We examine the parity violating terms generated by the box diagram in QED_3 at finite temperature. These lead to both extensive as well as non-extensive effective actions, which have very distinct behavior in the long wavelength and static limits. We discuss a large gauge Ward identity for the leading terms in the static limit, whose solution coincides with the effective action proposed earlier. 
F. T. Brandt, Ashok Das and J. Frenkel