Magnetic catalysis in a P-even, chiral-invariant three-dimensional model with four-fermion interaction

We study how an external magnetic field $H$ affects the phase structure of a P-even, chiral-invariant three-dimensional model of field theory with a four-fermion interaction. An arbitrarily small, but nonzero, magnetic field induces the spontaneous breaking of the initial symmetry (the magnetic catalysis phenomenon). Depending on the values of the coupling constants, the model vacuum is either P-even or chiral invariant for $H\neq0$.