Error in magnetisation of spin 1/2

Hi,

When calculating the magnetisation M of a spin 1/2 particle, we obtain However, the middle part is not equal to a tanh, but -tanh. Using the more formal definition of magnetisation M = -n\frac{dF}{dB}, we also obtain tanh. Therefore we are clearly missing a minus sign in the middle term of the above equation. This can be explained by the fact that, using our definition of the Zeeman hamiltonian without the minus sign, a spin up has a magnetic moment of -\mu_B and a spin down +\mu_B. In the middle term of the above equation, the prefactors -\mu_B and +\mu_B in front of the Boltzmann distributions in the numerator should thus be interchanged, indeed resulting once again in a tanh.

Best regards

closed via commit db82edab

Thanks, fixed!