Is it possible to calculate/estimate the value of the J parameter to be used in the Heisengerg/Ising hamiltonians?

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

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

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

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

• 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. – Xivi76 Jul 17 '20 at 18:09
• 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. – Camps Jul 19 '20 at 22:18
• 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. – Xivi76 Jul 19 '20 at 22:34
• Is this related? mattermodeling.stackexchange.com/a/104/88 – Thomas Jul 26 '20 at 3:27