Kittel, Ch2-2. Paramagnetism. Find the equilibrium value at temperature of the fractional magnetization M 2(s) Nm N of the system of N spins each of magnetic moment m in a magnetic field B. The spin excess is 2s. Take the entropy as the logarthithm of the multiplicity g(N,s) as given in (1.35): o(s)≈ log g(N,0) — for |s|<< N. Hint: Show that in this approximation o(U)=6₁ 25² with = logg(N,0). Further, show that T thermal average energy. N U² 2m² B²N U m² B²N' where U denotes (U), the
Kittel, Ch2-2. Paramagnetism. Find the equilibrium value at temperature of the fractional magnetization M 2(s) Nm N of the system of N spins each of magnetic moment m in a magnetic field B. The spin excess is 2s. Take the entropy as the logarthithm of the multiplicity g(N,s) as given in (1.35): o(s)≈ log g(N,0) — for |s|<< N. Hint: Show that in this approximation o(U)=6₁ 25² with = logg(N,0). Further, show that T thermal average energy. N U² 2m² B²N U m² B²N' where U denotes (U), the
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Transcribed Image Text:2. Kittel, Ch2-2. Paramagnetism. Find the equilibrium value at temperature of the
fractional magnetization
M
Nm
of the system of N spins each of magnetic moment m in a magnetic field B. The spin
excess is 2s. Take the entropy as the logarthithm of the multiplicity g(N,s) as given in
(1.35):
≈
o(s) log g(N,0) -
2(s)
N
o(U)=%
for s<< N. Hint: Show that in this approximation
with = logg (N,0). Further, show that
thermal average energy.
T
25²
N
U²
2m² B²N
==
U
m² B²N
2
where U denotes (U), the
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