center around the position of the peak $x_{m}$. Thus we can write $\beta\mu\left(x-x_{m}\right)/2x=\tilde{\beta}\left(x-x_{m}\right)$, where $\tilde{\beta}=1/k\tilde{T}\equiv\beta\mu/2x$ can be considered the corresponding *temperature* parameter, with defines the broadening of each exponential term in equation (\[Mt spin\]). This shows that the broadening depends not only on the real temperature $T$, but also on the Fermi energy $\mu$ and the magnetic field $x=1/B$. In this way we can get an estimation to how the temperature affects the observation of the spin splitting in the magnetization, which is dictated by how the width of the exponentials relates to the spin peaks separation $x_{2}-x_{1}=2\Delta$. This can be seen in figure \[fig5\], where for different temperatures it is shown the magnetization (left) and the exponentials that appear in equation (\[Mt spin\]) (right). Then we can identify four situations. In the first case, figure \[fig5\](a), the width is $<\Delta$ and one can clearly appreciate the spin splitting in the magnetization at $T\neq0$. The second case, figure \[fig5\](b), corresponds to the case when the width is $\Delta$, so the exponentials began to overlap. Then, for a width $>\Delta$ (but $<2\Delta$) in figure \[fig5\](c), the spin splitting effect starts to disappear, although one could still notice a small change of 