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The phenomenon of magnetic catalysis of chiral symmetry breaking in thequantum chromodynamic theory in the framework of logarithmic quark sigma modelis studied. Thermodynamic properties are calculated in the mean-fieldapproximation such as the pressure, the entropy density, the energy density,and measure interaction. The pressure, the entropy density, and the energydensity 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 anexternal magnetic field with absent of baryonic chemical potential whenexplicit symmetry breaking is included. A comparison is presented with theoriginal sigma model and other works. A conclusion indicates that thelogarithmic quark model enhances the magnetic catalysis phenomenon.

Thermo-magnetic Effects in an External Magnetic Field in the Logarithmic-Quark Sigma Model