the total magnetization of the NVBG is

$$\label{magnetizationtotal}
M = \frac{\kappa m}{\varepsilon(0,B)} N =d N.$$

The previous expression is expected because at $T\ll m$ all the particles are in the $s=1$ state. It is nothing else but the product of the effective magnetic moment by the particle density. However, an increase in the field still augment the magnetization because the effective magnetic moment $d$ grows with $B$ and diverges when $B\rightarrow B_c$ ($b \rightarrow 1$). Since $d$ is strictly positive for all values of $B$, the magnetization is always positive and different from zero even if $B=0$ ($M(B=0)=\kappa N$). This is an evidence of ferromagnetic response of the NVBG at low temperature. This behavior described for $M$ is shown in left panel of Fig. 5.

![\[fig3\] Magnetization as a function of magnetic field for several values of the particle density (left panel). We have also plotted the $B/4\pi$. The solutions of self-magnetization equation as a function of particle density (right panel).](mag3d.eps "fig:"){width="0.49\linewidth"} ![\[fig3\] Magnetization as a function of magnetic field for several values of the particle density (left panel). We have also plotted the $B/4\pi$. The solutions of self-magnetization equation as a function of particle density (right panel).](selfmag3d.eps "fig:"){width="0.49\linewidth"}

In 