  We study a planar four-Fermi Gross-Neveu model in the presence of a tilted
magnetic field, with components parallel and perpendicular to the system's
plane. We determine how this combination of magnetic field components, when
applied simultaneously, affects the phase diagram of the model. It is shown
that each component of the magnetic field causes a competing effect on the
chiral symmetry in these fermionic systems. While the perpendicular component
of the magnetic field tends to make the chiral symmetry breaking stronger, the
effect of the parallel component of the field in these planar systems is to
weaken the chiral symmetry through the enhancement of the Zeeman energy term.
We show that this competing effect, when combined also with temperature and
chemical potential, can lead to a rich phase diagram, with the emergence of
multiple critical points and reentrant phase transitions. We also study how the
presence of these multiple critical points and reentrant phases can manifest in
the quantum Hall effect. Our results provide a possible way to probe
experimentally chiral symmetry breaking and the corresponding emergence of a
gap (i.e., the presence of a nonvanishing chiral vacuum expectation value) in
planar condensed matter systems of current interest.
