  The phenomenon of magnetic catalysis of chiral symmetry breaking in the
quantum chromodynamic theory in the framework of logarithmic quark sigma model
is studied. Thermodynamic properties are calculated in the mean-field
approximation such as the pressure, the entropy density, the energy density,
and measure interaction. The pressure, the entropy density, and the energy
density increase with increasing temperature and an external magnetic field.
The critical temperature increases with increasing an external magnetic field.
In addition, the chiral phase transition is crossover in the presence of an
external magnetic field with absent of baryonic chemical potential when
explicit symmetry breaking is included. A comparison is presented with the
original sigma model and other works. A conclusion indicates that the
logarithmic quark model enhances the magnetic catalysis phenomenon.
