  The catalysis of chiral symmetry breaking by an applied constant magnetic
field and in the presence of boundaries along third axis is investigated in the
four-dimensional Nambu-Jona-Lasinio model. It is shown that in case of periodic
boundary conditions for fermions the magnetic field breaks the chiral symmetry,
generating a dynamical mass even at the weakest attractive interaction between
fermions. For antiperiodic boundary conditions the effect of the finite third
dimension is to counteract the chiral symmetry breaking.
