  Effects of external magnetic field on various properties of the quantum
chromodynamics under extreme conditions of temperature and density have been
analysed. To this end, we use SU(3) Polyakov linear sigma-model and assume that
the external magnetic field eB adds some restrictions to the quarks energy due
to the existence of free charges in the plasma phase. In doing this, we apply
the Landau theory of quantization. This requires an additional temperature to
drive the system through the chiral phase-transition. Accordingly, the
dependence of the critical temperature of chiral and confinement
phase-transitions on the magnetic field is characterized. Based on this, we
have studied the thermal evolution of thermodynamic quantities and the first
four higher-order moment of particle multiplicity. Having all these
calculations, we have studied the effects of magnetic field on chiral
phase-transition. We found that both critical temperature T_c and critical
chemical potential increase with increasing the magnetic field eB. Last but not
least, the magnetic effects of the thermal evolution of four scalar and four
pseudoscalar meson states are studied. We concluded that the meson masses
decrease as the temperature increases till T_c. Then, the vacuum effect becomes
dominant and rapidly increases with the temperature T. At low T, the scalar
meson masses normalized to the lowest Matsubara frequency rapidly decreases as
T increases. Then, starting from T_c, we find that the thermal dependence
almost vanishes. Furthermore, the meson masses increase with increasing
magnetic field. This gives characteristic phase diagram of T vs. external
magnetic field $B. At high T, we find that the masses of almost all meson
states become temperature independent. It is concluded that the various meson
states likely have different T_c's.

High Energy Physics - Phenomenology;High Energy Physics - Lattice