220
Appendix D: Analytical Expressions for χ(T )
E =−0.0035767 − 0.40837α + 3.4862α
2 − 0.73888α
3
F = 0.36184 − 0.065528α + 6.65875α
2 − 20.945α
3 + 15.425α
4
3. The uniform two-dimensional S = 1/2 Heisenberg lattice [3]
χ(T ) =
N A µ 2
B g 2
e
kT
5
n=1
a n J/kT
b n J/kT
n A n
B n
1 0.998586 −1.84279
2 1.28534
1.14141
3 0.656313 −0.704192
4 0.235862 −0.189044
5 0.277527 −0.277545
4. The generalized expression for a Heisenberg 2D lattice [4]
χ(T ) =
N A g 2
e µ B
3kT
Y 1 + Y 2
(1 − u 1 v 1 )(1 − u 2 v 2 )
with
Y 1 = (1 + u 1 v 1 )(1 + u 2 v 2 ) + (u 1 + v 1 )(u 2 + v 2 )
Y 2 = (u 1 + v 1 )(1 + u 2 v 2 ) + (u 2 + v 2 )(1 + u 1 v 1 )
u i = coth
S(S + 1)J i−
kT
−
kT
S(S + 1)J i−
v i = coth
S(S + 1)J i+
kT
−
kT
S(S + 1)J i+
5. Hexagonal 2D lattice [5, 6] (Fig. D.1)
χ(T ) =
N A g 2
e µ B
3kT
(1 + u 1 u 2 ) 2
1 + u 2
2
+ 2u 2 (1 + u 1 u 2 )
2 + u 1
1 − u 2
2
2
1 − u 2
1 u 2
2
1 − u 2
2
with
u i = coth
S(S + 1)J i
kT
−
kT
S(S + 1)J i