
Magnetic Systems 169
Therefore, the Curie law gives, for the difference C
B
e
−C
M
,
C
B
e
−C
M
=
aV B
2
e
T
2
(8.79)
which agrees with eqn(8.28), on using Curie law.
As another check on the model let us compute
∂
C
B
e
∂
B
e
and
∂
C
M
∂
M
. Explicit
evaluation yields
∂
C
B
e
∂
B
e
=
2aV B
e
T
2
= T
∂
2
∂
T
2
M
B
e
(8.80)
∂
C
M
∂
M
=0=−T
∂
2
∂
T
2
B
e
M
(8.81)
In obtaining the second equation we used the fact that B
e
is linear in T when M is
held fixed. This is in accord with eqn.(8.21).
8.2.6 Equilibrium conditions
Now we briefly discuss the connection between the magnetic thermodynamic poten-
tials and the criterion for equilibrium for magnetic systems. As far as the Helmholtz
free energy is concerned, th