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It is shown that in $2+1$ dimensions, a constant magnetic field is a strongcatalyst of dynamical flavor symmetry breaking, leading to generating a fermiondynamical mass even at the weakest attractive interaction between fermions. Theeffect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. Thelow-energy effective action in this model is derived and the thermodynamicproperties of the model are established. The relevance of this effect forplanar 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

Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in 2 + 1 Dimensions