Yes, this topic is pretty mature I believe to FM and AFM by using quantum mechanics and specifically density functional theory. More specifically, the mean-field theory and Ising directions are essential to calculate phase transition temperature in ferromagnetic or anti-ferromagnetic materials. I'm not going to go through all the mathematical details here, which is beyond the scope of this SE I believe, but you could find the more solid theoretical background of this topic from outstanding work of Gyorffy et. al. that described how one could construct a self-consistent model based on Pauli equation and derive the magnetic momentum field from first-principle calculations.