  The chiral symmetry breaking in the presence of external magnetic field is
studied in the framework of logarithmic quark-sigma model. The effective
logarithmic mesonic potential is employed and is numerically solved in the
mean-field approximation. We find that the chiral symmetry breaking enhances in
comparison with the original sigma model. Two sets of parameterization are
investigated in the present model. We find that increasing coupling constant
enhances the breaking symmetry while increasing sigma mass inhibits enhancing
chiral broken vacuum state. A comparison with the Numbu-Jona-Lasinio model and
the Schwinger-Dyson equation is discussed. We conclude that the logarithmic
sigma model enhances the magnetic catalysis in comparison with the original
sigma model and other models.
