Magnetization Fluctuation
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 42
30-8-2016
1531
Magnetization Fluctuation
Consider N moments μ with two allowed orientations ±μ in an external field H at temperature τ. Calculate the fluctuation of magnetization M, i.e.,
SOLUTION
The energy of a dipole in a magnetic field εm may be written
The partition function Z is simply
(1)
Since the moments are all independent, we may express the average magnetization ⟨M⟩ as
(2)
On the other hand,
(3)
For i ≠ j the ensemble averages are independent, and
We are left with i = j so (2) and (3) give
(4)
We then obtain
(5)
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