Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $E_0 < E_f$.

Is there a good method to solve such a problem with not too much calculation power? And in the end i want to play around with both potentials and see how the number of electron is changing for each situation.

Thanks for any advice,

/no

PS: i already asked a question concerning to my code i wrote in SO, but i was rethinking the method of mine for solving this problem. I did an iterative attempt and reformulated the equation for a root searching algorithm and varied the energy difference $E_0 - E_f$. The programming stuff is on ipython plus a result of one simualtion run.

share|cite|improve this question
    
I suggest you try asking this on scicomp.stackexchange.com – David Ketcheson Jan 13 '12 at 20:12

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.