Electron-gas spin polarization ($\zeta$)

For number densities $n_{\uparrow },n_{\downarrow }$, $\zeta =(n_{\uparrow }-n_{\downarrow })/(n_{\uparrow }+n_{\downarrow })$. Uniform spin polarization raises kinetic energy by concentrating occupation in one Fermi sphere, while lowering exchange energy.