Competition between paramagnetism and diamagnetism in charged Fermi gases

The charged Fermi gas with a small Lande-factor $g$ is expected to be diamagnetic, while that with a larger $g$ could be paramagnetic. We calculate the critical value of the $g$-factor which separates the dia- and para-magnetic regions. In the weak-field limit, $g_c$ has the same value both at high and low temperatures, $g_c=1\mathrm{/}\sqrt{12}$. Nevertheless, $g_c$ increases with the temperature reducing in finite magnetic fields. We also compare the $g_c$ value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels $\sigma =\pm 1,0$, and find that $g_c$ of Bose and Fermi gases is larger and smaller than that of Boltzmann gases, respectively.