Dear Prof Simon,
In equation 4.13 you claim that the magnetization is the difference [# up spins] - [# down spins] times my/V. Later you show that this difference is a (linear) function of B.
In taking the derivate dE/dB in the way you did, you assumed that the difference is not a function of B. In fact it is and E should be therefore propotional to B^2.
I therefore believe that your result is incorrect and there should be a factor of 2 in front.
What do you think?
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