Magnetic Fields in Quantum Degenerate Systems and in Vacuum

We consider self-magnetization of charged and neutral vector bosons bearing a magnetic moment in a gas and in vacuum. For charged vector bosons (W bosons) a divergence of the magnetization in both the medium and the electroweak vacuum occurs for the critical field B=B_{wc}=m_{w}^{2}/e. For B>B_{wc} the system is unstable. This behavior suggests the occurrence of a phase transition at B=B_{c}, where the field is self-consistently maintained. This mechanism actually prevents $B$ from reaching the critical value B_{c}. For virtual neutral vector bosons bearing an anomalous magnetic moment, the ground state has a similar behavior for B=B_{nbc}=m_{nb}^{2}/q . The magnetization in the medium is associated to a Bose-Einstein condensate and we conjecture a similar condensate occurs also in the case of vacuum. The model is applied to virtual electron-positron pairs bosonization in a magnetic field B \sim B_{pc}\lesssim 2m_{e}^{2}/e, where m_e is the electron mass. This would lead also to vacuum self-magnetization in QED, where in both cases the symmetry breaking is due to a condensate of quasi-massless particles.