on the abscise axis can be computed as a function of $b$

$$\label{Tc-1D}
T_{max} = \frac{(\zeta (\frac{3}{2}) N)^2}{144 \varepsilon(0,B)}.$$

As $T_{cond}$, $T_{max}$ increases with the density and diverges with the magnetic field. Left panel of Fig. 4 shows $T_{max}$ as a function of $b$ for $N = 10^{34}cm^{-3}$. Although the condensed and not condensed region were shaded, it is worth not to forget that $T_{max}$ does not define a critical temperature. Therefore, left panel of Fig. 4 is only an approximate phase diagram whose provides a range of temperatures around which the population of the ground state starts to grow. The values of these temperatures are in the order of those of several astronomical objects.

![\[fig4\] The specific heat as a function of the temperature (left panel); $T_{max}$ vs. $b$. (right panel). In both graphics $N= 10^{34} cm^{-3}$](C-1D.eps "fig:"){width="0.5\linewidth"} ![\[fig4\] The specific heat as a function of the temperature (left panel); $T_{max}$ vs. $b$. (right panel). In both graphics $N= 10^{34} cm^{-3}$](dfases-1D.eps "fig:"){width="0.5\linewidth"}

Magnetization
-------------

We can obtain the magnetization of the three and one dimensional systems from Eq. (\[Grand-Potential-Tcero\]) and Eq. (\[Grand-Potential-2DstTcero\]) if we derive in both expressions with respect to the magnetic field

$$\label{magnetization}
M = d N_0 