As is the case for most lattice models in statistical mechanics, there are no known exact solutions to the Z N model in three dimensions. In two dimensions, however, it is exactly solvable on a square lattice for certain values of N and/or the 'weights' x k . Perhaps the most well-known example is the Ising model, which admits spins in two opposite directions (i.e. s r = ± ± 1 ). This is precisely the Z N model for N = 2 , and therefore the Z N model can be thought of as a generalization of the Ising model. Other exactly solvable models corresponding to particular cases of the Z N model include the three-state Potts model, with N = 3 and x 1 = x 2 = x c , where x c is a certain critical value (FZ), and the critical Askin–Teller model where N = 4 .