What is the Hamiltonian for a 2D Ising model on a square lattice?

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Homework Statement


Consider a 2 dimensional three state Ising model with ferromagnetic coupling J, where si = −1, 0, 1
in a magnetic field h on a triangular lattice. Construct a mean field equation for the magnetization m.

The Attempt at a Solution


I don't know how to start. 2d ising model on a triangular lattice? I need some hamiltionian to start with, I'm not sure what that would look like, and then continue with makeing a mean field theory approximation, getting a partition function and so on
 
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2d lattice ising model

I have the same problem, but for a square lattice. (For a take home final due monday 9am. :frown: ) Do you know what the Hamiltonian for that would look like?
 

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