  SU($3$) Polyakov linear-sigma model (PLSM) is systematically implemented to
characterize the quark-hadron phase structure and to determine various
thermodynamic quantities and magnetization of the QCD matter. In mean-field
approximation, the dependence of the chiral order-parameter on finite magnetic
field is also calculated. In a wide range of temperatures and magnetic field
strengths, various thermodynamic quantities including trace anomaly, speed of
sound squared, entropy density, specific heat are presented and some magnetic
properties are described, as well. Wherever available these results are
confronted to recent lattice QCD calculations. The temperature dependence of
these quantities confirms our previous result that the transition temperature
is reduced with the increase in the magnetic field strength, i.e. QCD matter is
to be characterized by an inverse magnetic catalysis. Furthermore, the
temperature dependence of the magnetization shows that the conclusion that the
QCD matter has paramagnetic properties slightly below and far above the
pseudo-critical temperature, is confirmed, as well. The excellent agreement
with recent lattice calculations proves that our QCD-like approach (PLSM) seems
to possess the correct degrees-of-freedom in both hadronic and partonic phases
and describes well the dynamics deriving confined hadrons to deconfined
quark-gluon plasma.
