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

摘要

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.