  We review the spontaneous magnetization of the vacuum of non-Abelian gauge
fields at high temperature. The standard model of particles is investigated as
a particular example. By using both analytic methods of quantum field theory
and gauge field theory on a lattice, we determine the Abelian (chromo)magnetic
fields in the restored phase of the model at high temperatures $T \geq T_{ew}$.
The fields are stable and temperature dependent, $B = B(T)$. We investigate the
mechanisms of the field stabilization in detail. The screening parameters for
electric and magnetic fields - the Debye, $m_D(B,T),$ and magnetic,
$m_{magn.}(B,T)$, masses - are calculated. It is shown that, in the field
presence, the former one is smaller than at zero field. The magnetic mass of
the (chromo)magnetic fields is determined to be zero, as for usual $U(1)$
magnetic field. We also show that the vacuum magnetization stops at
temperatures below the electroweak phase transition temperature, $T \leq
T_{ew}$, when a scalar condensate creates. These properties make reasonable a
possibility that the intergalactic magnetic fields observed recently were
spontaneously generated in the hot Universe at the reheating epoch due to
vacuum polarization of non-Abelian gauge fields. We present a procedure for
estimating the field strengths $B(T)$ at different temperatures. In particular,
the value of $B(T_{ew}) \sim 10^{14} G$, at $T_{ew}$ is estimated with taking
into consideration the observed intergalactic magnetic field $B_0 \sim 10^{-
15} G$. The magnetic field scale is also estimated. Some model dependent
peculiarities of the phenomena studied are briefly discussed.
