the seek of one of our main motivations, the search for astrophysical magnetic field sources, we are interested in exploring if the system reaches the self-magnetization condition, i.e. whether or not the solid line in left panel of Fig. 5 intersects the curves of the magnetization. To do that we consider $H = B-4 \pi M$ with no external magnetic field $H=0$, and solve the self-consistent equation $B=4\pi M$. This is a cubic equation due to the non linear dependency of the magnetization on the field. In right panel of Fig. 5 its three solutions have been plotted but only one of them is physically meaningful. For one of the roots, the magnetic field is negative (see dotted line), while for another, it decreases with the increasing density, reaching $B_c$ when $N$ goes to zero (dot dashed line). These solutions implies that the magnetization also decreases with $N$, hence, they are contrary to Eq. (\[magnetizationtotal\]) and must be discarded. Therefore, the only admissible solution of the self-magnetization equation is the one given by the solid line. The points of this line are the values of the self-maintained magnetic field. Nevertheless, this solution becomes complex for densities higher than $N_c = 