  We consider the effect of the photon radiative correction on the vacuum
energy in a superstrong magnetic field. The notion of a photon anomalous
magnetic moment is analyzed and its connection with the quasiparticle character
of the electromagnetic radiation is established. In the infrared domain the
magnetic moment turns out to be a vector with two orthogonal components in
correspondence with the cylindrical symmetry imposed by the external field. The
possibility of defining such quantity in the high energy limit is studied as
well. Its existence suggests that the electromagnetic radiation is a source of
magnetization to the whole vacuum and thus its electron-positron zero-point
energy is slightly modified. The corresponding contribution to the vacuum
magnetization density is determined by considering the individual contribution
of each vacuum polarization eigenmode in the Euler-Heisenberg Lagrangian. A
paramagnetic response is found in one of them, whereas the remaining ones are
diamagnetic. Additional issues concerning the transverse pressures are
analyzed.
