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The linear-sigma model, in which information about confining gluons isincluded through the Polyakov-loop potential (PLSM), is considered in order toperform a systematic study for various magnetic properties of QCD matter underextreme conditions of high temperatures and densities and finite magnetic fieldstrengths. The introduction of magnetic field to the PLSM Lagrangian requiressuitable utilization of Landau quantization, modification in the dispersionrelations, and momentum-space dimension-reduction. We observed that increasingthe magnetic field leads to filling-up lower Landau levels first and decreasingthe number of occupied levels. We conclude that the population of Landau levelsis most sensitive to the magnetic field and to the quark charges. Theinfluences of finite magnetic field on the temperature dependence of chiral anddeconfinement order-parameter(s) are studied. We present estimations for themagnetization, the magnetic susceptibility, the permeability and the catalysisproperties of QCD matter as functions of temperature. The dependences of theresulting freezeout parameters, temperatures and baryon chemical potentials onthe corresponding magnetic field strengths have been analyzed, as well. Thesecalculations are compared with recent lattice QCD simulations, wheneveravailable. We conclude that the QCD matter seems to have paramagnetic propertyat temperatures greater than the critical one. There is an evidence for weakdiamagnetic property at low temperatures. Last but not least, we observe thatthe magnetic catalysis is inverse, namely the critical temperatures decreasewith increasing the magnetic field.

SU(3) Polyakov linear-sigma model: Magnetic properties of QCD matter in thermal and dense medium