Posted by Banana on April 3, 2013, 6:05 pm, in reply to "paramagnestism for general J"
If you want to be convinced that you can do it later, I think I've managed to go through it correctly. Let x =(beta * g * B * mu_b). The partition function can be written as (e^Jx  e^(J+1)x)/(1e^x) = sinh(x(J+1/2))/sinh(x/2) dF/dB = k_B*T(coth((x/B)(J+1/2))  coth ((x/B)(J1/2))) Making the small B expansion we have dF/dB = k_B*T[1/B  1/B + (x^2/3B)*((J+1/2)^2  (1/2)^2)] = k_B*T(x^2/B)(J(J+1))/3 And then just differentiate wrt B and multiply by n*mu_0. 
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