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

$$E_{T}=\sum_{k,\sigma}E_{\sigma}(k)=\sum_{k}E_{\uparrow}(k)=E_{kin}+N I$$.

In general we have

$$E_{T}=\sum_{k,\sigma}E_{\sigma}(k)=\sum_{k,\sigma}\epsilon(k)+\sum_{\sigma}\sigma N_{\sigma} I P=E_{kin}+N I P^{2}$$.

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)