Take the 2-minute tour ×  I'm trying to simulate the
degenerative Anderson model. So depending on an energy
difference first orbital and afterwards spin magnetism occurs.
First i try to solve an easier ansatz with a limitation of only
two orbitals to $l_z = \pm 1$. In this case i end up with a set
of 4 equations:  $\Delta \tan^{-1} (1/\pi * n_{m \sigma}) = E_0-
E_f+(U-
J)n_{\overline{m}\sigma}+U(n_{1\overline{\sigma}}+n_{2\overline{
\sigma}})$  Where here $\sigma$ is the direction of the spin of
certain electron in the orbital $m$, here only $1,2$ and the
overline always is the opposite. U is a Hubbard potential and
$J$ an intraatomic exchange. So we gathered a self consistent
set of non-linear equation and i want to find solution in terms
of $n_{m \sigma}$ satisfying all 4 equations. I already did some
simulation and were able to plot it on dependancy of the energy
difference with respect to the fermi energy, which is my
parameter. So i change it in a certain range and one finds
magnetic solution for $E_0 < E_f