Theoretically, one often use the spin-spin correlation function (which is the sum of 3 terms in the x, y, z directions) to describe ferromagnetic (FM) or anti-ferromagnetic (AFM) order. For example, on the square lattice,

  • If tends to a positive value as the separation between i, j tends to infinity, we say there is FM order;
  • If changes sign alternatively as j changes between the two sub-lattices (with spin up and spin down), we say there is AFM order.

I want to know if there are other spin correlation functions that can help identify more complicated magnetic order, such as spin-canting and ferrimagnetism?

(Visualization of these orders can be found at, e.g. https://web.archive.org/web/20160611194326/http://magician.ucsd.edu/essentials/WebBookse18.html)

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