The axial symmetry of the magnetic field is reflected in the particle spectra and in the energy-momentum tensor of the system which becomes anisotropic. For that reason, we also study the splitting of the parallel and perpendicular pressures with respect to the direction of the magnetic field.

Our paper is organized as follows. In Section \[eom\], we present the equation of motion and spectrum of neutral vector boson with MM. Section \[thermo\] contains a derivation of the thermodynamical potential, particle density, BEC, internal energy, entropy and specific heat for the three and one dimensional NVBG. Magnetization, self-magnetization and anisotropic pressures are also discussed. Section \[conclusions\] is devoted to conclusions. Appendix A and B contains some details of the calculations.

Equation of motion of a neutral vector boson bearing a magnetic moment {#eom}
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Neutral spin-one bosons with magnetic moment that moves in a magnetic field can be described by an extension of the original Proca Lagrangian for spin one particles that includes particle-field interactions [@PhysRev.131.2326; @PhysRevD.89.121701]

$$\begin{aligned}
\label{Lagrangian}
  L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\frac{1}{2} \rho^{\mu\nu}\rho_{\mu\nu}
       + m^2 \rho^{\mu}\rho_{\mu}
      +i m \kappa(\rho^{\mu} \rho_{\nu}-\rho^{\nu}\rho_{\mu}) F_{\mu\nu}.\end{aligned}$$

In Eq. (\[Lagrangian\]) the indices $\mu$ and $\nu$ run from 1 to 4, $F^{\mu\nu}$ is the electromagnetic tensor, and $\rho_{\mu\nu}$, 