Clock model

The clock model places a planar unit vector at every lattice site but restricts its angle to finitely many equally spaced values. Nearest-neighbour spins usually interact through the cosine of their angular difference.

The four-state clock model permits the four angles $0,\pi /2,\pi ,3\pi /2$. Its finite discrete symmetry allows finite-temperature long-range order above one spatial dimension.

The XY model is the infinite-state limit of the clock model: each spin is a unit vector with a continuous angle and the global symmetry is $O(2)$.