- #1

kde2520

- 16

- 0

Hi,

Studying for my thermal physics final and want to make sure I'm doing this right as our book doesn't have answers. Pretty simple question so I need to make sure I'm doing the basics right.

Find the equilibrium value at temperature [tex]\tau[/tex] of the fractional magnetization

[tex]\frac{M}{Nm} = \frac{2<s>}{N}[/tex]

of the system of N spins each of magnetic moment m in a magnetic field B. The spin excess is 2s. Take the ntropy as the logarithm of the multiplicty g(N,S) where

[tex]{\sigma}(s) \approx {\sigma}_o - \frac{2s^2}{N}[/tex]

where [tex]{\sigma}_o = \ln{g(N,0)}[/tex] and g is the multiplicity function. Using the fact that U = 2smB, we can say

[tex]{\sigma}(U) = {\sigma}_o - \frac{U^2}{2m^2B^2N}[/tex]

Now, the equilibrium of the system will occur when the entropy is maximized, so I take the derivative with respect the U, set it equal to zero, solve for U and then use that to find s. This gives me that <s> = 0 which makes sense as the temperature isn't going to affect whether you have spin up or spin down, right?

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