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What is the state of art technique in solving exact ground state of Heisenberg model, meaning minimization of the H terms (hamiltonian) provided infinite spin space?

http://en.wikipedia.org/wiki/Classical_Heisenberg_model

I read that there is a method called Bethe Ansatz. But as Ansatz suggests, is it a mathematical method or just some heuristics? Thank you. Are there some modern exposition of Bethe Ansatz or other methods to solve the exact ground state problem? Thank you.

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  • $\begingroup$ The method called "Bethe Ansatz" applies to quantum models, not to classical spin models. The classical Heisenberg model in two or more dimensions, in a nonzero magnetic field, has no exact solution, as far as I know. $\endgroup$
    – Carlo Beenakker
    Feb 6, 2015 at 7:14
  • $\begingroup$ Thank you very much for your response.... actually, rather than finding the exact partition function. What we want is the ground state configurations of spins.... $\endgroup$
    – user40780
    Feb 6, 2015 at 15:51
  • $\begingroup$ physics.stackexchange.com/q/163658/24498. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. $\endgroup$
    – D.W.
    Apr 28, 2016 at 4:48

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