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Date: 11-8-2016
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Date: 10-9-2016
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Date: 9-8-2016
4005
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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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