Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in 2+12+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.Comment: 11 pages, LaTeX. The final version (with minor corrections) which appeared in Phys.Rev.Lett. 73 (1994) 349