  The effect of the higher-order mesonic interactions is investigated on the
chiral symmetry breaking in the presence of an external magnetic field. The
effective of higher-order mesonic potential is employed and is numerically
solved in the mean-field approximation. The chiral symmetry breaking increases
with increasing magnetic field. Two sets of free parameterization are
investigated on the magnetic catalysis. A comparison is discussed with the
original sigma model and other studies. The obtained results are included that
the higher-order mesonic interactions play an important role in the magnetic
catalysis.
