  In quark-gluon plasma (QGP), at higher deconfinement temperatures $T \ge T_d$
the spontaneous generation of color magnetic fields, $b^3(T), b^8(T) \not = 0$
(3, 8 are color indexes), and usual magnetic field $b(T) \not = 0$ happens.
Simultaneously, the Polyakov loop and/or algebraically related to it $A_0(T)$
condensate, which is solution to Yang-Mills imaginary time equations, are also
created. Usually, in analytic quantum field theory these effects are
investigated independently of each other within the effective potentials having
different mathematical structures. The common generation of these condensates
was detected in lattice Monte Carlo simulations.
  Recently, with the new type two-loop effective potential, which generalizes
the known integral representation for the Bernoulli polynomials and takes into
consideration the magnetic background, this effect has been derived
analytically.
  The corresponding effective potential W(T, b^3, A_0 ) was investigated either
in SU(2) gluodynamics or full QCD. The gauge fixing independence of it was
proved within the Nielsen identity approach. The values of magnetic field
strengths at different temperatures were calculated and the mechanism of
stabilizing fields due to A_0(T) condensate has been discovered. In the present
review, we describe this important phenomenon in more details, as well as a
number of specific effects - induced color charges, effective
photon-photon-gluon vertexes - happening due to vacuum polarization at this
background. They could serve as the signals of the QGP creation in the heavy
ion collision experiments.
  Key words: spontaneous magnetization, high temperature, asymptotic freedom,
effective potential, A_0 condensate, effective charge, effective vertexes.
