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

[WarnK]

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

 

[winkerbean]

2d lattice ising model

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