coupling between the neutral mesons and the magnetic field. More recently, BEC for an gas of interacting vector bosons at zero magnetic field was studied in [@Satarov:2017jtu].

Hence, the aim of this paper is to study the thermodynamical properties of a neutral vector boson gas (NVBG) in a constant magnetic field. We will concern with its phenomenology in the framework of Proca theory and independently of the realistic conditions in which it may appear. Neutral vector bosons can be mesons, atoms and other paired fermions with total integer spin. For numerical calculations we use a positronium gas parameters, characterized by a mass approximately $2 m_e$, ($m_e$ is the electron mass) and twice the electron magnetic moment $\kappa = 2\mu_B $ being $\mu_B$ the Bohr magneton. Since we are focussed on possible astrophysical applications we deal with systems of densities in the range of $10^{30}-10^{34}cm^{-3}$.

The thermodynamical properties of the NVBG are studied in three and one dimensions. The BEC phase transition turns out to be diffuse in one dimension and usual in three. In both cases, for low enough temperatures self-magnetization arises. An analysis of this phenomenon lead us to the conditions for the appearance of a self sustained field. 