= Stoner criterion
{c}
{title2=$U_c\chi_0=1,\quad\chi_0=\int\nu(-n_F^{\prime})d\epsilon$}
In the homogeneous spin-vector mean-field scheme with field cost $M^2/(2U)$ and <spin-summed density of states> per site, the paramagnetic curvature is proportional to $U^{-1}-\int\nu(\epsilon)[-n_F'(\epsilon)]d\epsilon$. It changes sign at $U\chi_0=1$. For a smooth low-temperature <density of states>, $\chi_0\simeq\nu(\mu)$, giving the familiar Fermi-level criterion. Interaction and spin-counting conventions must be specified before comparing coefficients.
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