Itinerant Spin Dynamics in Structures of ... - Jacobs University
Itinerant Spin Dynamics in Structures of ... - Jacobs University
Itinerant Spin Dynamics in Structures of ... - Jacobs University
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Appendix E: Summation over the Fermi Surface 149<br />
This gives us<br />
f 1 = 2 N−1<br />
∑<br />
πN<br />
s=1<br />
f 2 = 2<br />
πN<br />
f 3 = 2<br />
πN<br />
f 4 = 2<br />
πN<br />
f 5 = 2<br />
πN<br />
s 2<br />
N<br />
√1− ( ) , (E.9)<br />
2 s 2<br />
N<br />
√ N∑ ( s<br />
) 2,<br />
1−<br />
(E.10)<br />
N<br />
s=1<br />
N∑ ( s<br />
)<br />
√<br />
2 ( s<br />
) 2,<br />
1−<br />
(E.11)<br />
N N<br />
s=1<br />
N∑ ( s<br />
)<br />
√<br />
4 ( s<br />
) 2,<br />
1−<br />
(E.12)<br />
N N<br />
s=1<br />
N∑<br />
s=1<br />
Writ<strong>in</strong>g Eq.(E.1) <strong>in</strong> a compact way gives us Eq.(4.49).<br />
( ( )3<br />
s 2 ( s 2 2<br />
1− . (E.13)<br />
N)<br />
N)
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