Extended ising model ground state configuration algorithm

[Key01023]

Extended ising model ground state configuration algorithm

 

Is there a general solver (or theoretical algorithm) for ground state configuration of extended ising model, which involves arbitrary lattice, arbitrary number(3,4,5) body interactions and arbitrary Hamiltonia, and arbitrary number of spin(-1,0,1 and so forth) ? Except exact enumeration, what could we do better? Could this problem be translated as an optimization problem?

 

I know such requirement is too stringent. But is there some research or established knowledge that aims to accomplish this?

[TrappedLight]

It's been a long time since I have read anything on the Ising model, so best I keep my mouth shut.