Talk:Stoner criterion

Sign error?

Shouldn't the sign before the $I$ in

$E_{\uparrow }(k)=\epsilon (k)+I{\frac {N_{\uparrow }-N_{\downarrow }}{N}},\qquad E_{\downarrow }(k)=\epsilon (k)-I{\frac {N_{\uparrow }-N_{\downarrow }}{N}}$

be the other way around? If we for example assume a fully polarized state with $N_{\uparrow }=N,N_{\downarrow }=0$, then we get

$E_{\uparrow }(k)=\epsilon (k)+I,\qquad E_{\downarrow }(k)=\epsilon (k)-I,$

with the total energy

$E_{T}=\sum _{k,\sigma }E_{\sigma }(k)=\sum _{k}E_{\uparrow }(k)=E_{kin}+NI$.

In general we have

$E_{T}=\sum _{k,\sigma }E_{\sigma }(k)=\sum _{k,\sigma }\epsilon (k)+\sum _{\sigma }\sigma N_{\sigma }IP=E_{kin}+NIP^{2}$.

But that means that the polarization will always increase the total energy. Only a negative $I$ can lead to ferromagnetism.Jan Krieg (talk) 14:55, 9 April 2014 (UTC)

It would appear that the above problem with the article was fixed sometime in the past. So this is no longer an issue. 67.198.37.16 (talk) 17:09, 15 May 2024 (UTC)