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Studying magnetic systems, two frequently used approximations are the Heisenberg and Ising models (a discussion about these approximations can be read here):

\begin{equation} \tag{Heisenberg} \hat{H}_H=-\sum_{\langle i j\rangle}J\hat{S}_i\hat{S}_j \end{equation}

\begin{equation} \tag{Ising} \hat{H}_I=-\sum_{\langle ij\rangle}J\hat{S}_i^z\hat{S}_j^z \end{equation}

Is there a theoretical method/way to determine realistic values for the $J$ parameter?

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  • $\begingroup$ If by J you mean inter-site exchange (the angular brackets under the summation refer to nearest neighbours), then refer to this question that I asked earlier : mattermodeling.stackexchange.com/questions/1359/…. If you are talking in the context of DFT, J is usually taken to be 0-20% of the Hubbard U as a thumb rule. $\endgroup$ – Xivi76 Jul 17 '20 at 18:09
  • $\begingroup$ Thanks @Xivi76. Yes, it is related to the inter-site exchange but I think that it is slightly different as it is just for spins (as individual entities) and not for electrons. $\endgroup$ – Camps♦ Jul 19 '20 at 22:18
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    $\begingroup$ It's quantifiable in the same way as the hubbard 'U'. Even the Hubbard 'U' is dependent on the spin operator. There are plenty of notes that explain this. $\endgroup$ – Xivi76 Jul 19 '20 at 22:34
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    $\begingroup$ Is this related? mattermodeling.stackexchange.com/a/104/88 $\endgroup$ – Thomas♦ Jul 26 '20 at 3:27

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