= Pauli moment of a massless electron gas
{c}
{title2=$\mathcal M=3N\mu^2B/(cp_F)+O(B^3)$}
For noninteracting spin-half particles with dispersion $E=cp$, the two spin populations at common chemical potential $\varepsilon$ are $V(\varepsilon\pm\mu B)^3/(6\pi^2\hbar^3c^3)$. Fixed total number changes $\varepsilon$ only at quadratic order in $B$. Their population difference is therefore $3N\mu B/(cp_F)$ to first order, giving the displayed magnetic moment. Only the specified spin-energy splitting is included, not orbital magnetic effects.
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