Spins have only two states, 
or 
.
Energy is given by
= spin at site i of crystalline lattice
= nearest neighbors in the lattice
J = interaction strength
,
spins aligned
,
spins not aligned
If J > 0, the state of lowest energy is when all spins are aligned. This is called a ferromagnet.
J < 0 is an antiferromagnet, which also occurs in real systems (will come back to this later).