magnetized and undergoes a phase transition to a diffuse BEC [@ROJAS1996148; @PEREZROJAS2000].

For a diffuse phase transition there is not a critical temperature, but an interval of temperatures along which it occurs gradually [@ROJAS1997]. In particular, a diffuse BEC phase is characterized by the presence of a finite fraction of the total particle density in the ground state and in states on its neighborhood at some temperature $T>0$. In this sense, the criterion for defining a diffuse BEC is weaker than the used for the usual one, which requires the existence of a critical temperature below which there is a macroscopic amount of particles in the ground state. Whether a BEC is usual or diffuse is strongly related to the dimension of the system [@ROJAS1997].

Although both, charged and neutral vector bosons, could be relevant participants of astronomical phenomena, the thermodynamics of the neutral vector boson gas has been less studied. An effect analogous to self-magnetization, named BE-ferromagnetism, was founded in [@Yamada] for a gas of non relativistic ideal neutral boson with spin one. In [@Chernodub:2010qx] and [@Chernodub:2012fi] magnetic field induced superconductivity and superfluidity are obtained for a gas of charged an neutral vector mesons, but it ignores the weak 