Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in   $2+1$ Dimensions
  It is shown that in $2+1$ dimensions, a constant magnetic field is a strong catalyst of dynamical flavor symmetry breaking, leading to generating a fermion dynamical mass even at the weakest attractive interaction between fermions. The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The low-energy effective action in this model is derived and the thermodynamic properties of the model are established. The relevance of this effect for planar condensed matter systems is pointed out. 
V.P.Gusynin, V.A.Miransky, and I.A.Shovkovy