3.1. Mean field theory for anti-ferromagnetic systems

a. Prove that the mean field theory can be applied to anti-ferromagnetic systems defined on a square lattice.

b. Generalize this result to all lattices that admit two sub-lattices such that the nextneighbour sites of one are sites of the other, and vice versa. This occurs, for instance, in the two dimensional exagonal or square lattices.

c. What happens if we consider a triangular lattice?