  The linear-sigma model, in which information about confining gluons is
included through the Polyakov-loop potential (PLSM), is considered in order to
perform a systematic study for various magnetic properties of QCD matter under
extreme conditions of high temperatures and densities and finite magnetic field
strengths. The introduction of magnetic field to the PLSM Lagrangian requires
suitable utilization of Landau quantization, modification in the dispersion
relations, and momentum-space dimension-reduction. We observed that increasing
the magnetic field leads to filling-up lower Landau levels first and decreasing
the number of occupied levels. We conclude that the population of Landau levels
is most sensitive to the magnetic field and to the quark charges. The
influences of finite magnetic field on the temperature dependence of chiral and
deconfinement order-parameter(s) are studied. We present estimations for the
magnetization, the magnetic susceptibility, the permeability and the catalysis
properties of QCD matter as functions of temperature. The dependences of the
resulting freezeout parameters, temperatures and baryon chemical potentials on
the corresponding magnetic field strengths have been analyzed, as well. These
calculations are compared with recent lattice QCD simulations, whenever
available. We conclude that the QCD matter seems to have paramagnetic property
at temperatures greater than the critical one. There is an evidence for weak
diamagnetic property at low temperatures. Last but not least, we observe that
the magnetic catalysis is inverse, namely the critical temperatures decrease
with increasing the magnetic field.
