Dynamical Flavour Symmetry Breaking by a Magnetic Field in Lattice QED_3
  We perform a lattice study, in the quenched approximation, of dynamical mass generation in a system of relativistic (Dirac) fermions, coupled to an Abelian gauge field in (2+1)-dimensions, in the presence of an external (constant) magnetic field, perpendicular to the spatial planes. It is shown that a strong magnetic field catalyzes chiral symmetry breaking, in agreement with results in the continuum. The r\^ole of the higher-Landau poles in inducing a critical temperature above which the phenomenon disappears is pointed out. We also discuss the implications of this model on the opening of a gap in doped antiferromagnetic superconductors. 
K. Farakos, G. Koutsoumbas and N.E.Mavromatos