= Homogeneous spin-field effective action
{title2=$S_{\rm eff}=\beta NM^2/(2U)-\sum_{k\sigma}\ln[1+e^{-\beta(\epsilon_k-\mu-\sigma M)}]$}
Integrating free <fermions> in a constant auxiliary spin field gives $S_{\rm eff}=\beta NM^2/(2U)-\sum_{k\sigma}\ln[1+e^{-\beta(\epsilon_k-\mu-\sigma M)}]$. Differentiation gives the self-consistent spin polarization. The extensive action is a mean-field restriction of the full auxiliary-field functional integral, not an exact omission of all spatial/time fluctuations.
Back to article page
