Editing Potts model (section)

=== Vector Potts model ===
The Potts model consists of ''spins'' that are placed on a [[lattice (group)|lattice]]; the lattice is usually taken to be a two-dimensional rectangular [[Euclidean space|Euclidean]] lattice, but is often generalized to other dimensions and lattice structures.

Originally, Domb suggested that the spin takes one of <math>q</math> possible values {{Citation needed|date=May 2022}}, distributed uniformly about the [[circle]], at angles
: <math>\theta_s = \frac{2\pi s}{q},</math>
where <math>s = 0, 1, ..., q-1</math> and that the interaction [[Hamiltonian mechanics|Hamiltonian]] is given by
: <math>H_c = J_c\sum_{\langle i, j \rangle} \cos \left( \theta_{s_i} - \theta_{s_j} \right)</math>
with the sum running over the nearest neighbor pairs <math>\langle i,j \rangle</math> over all lattice sites, and <math>J_c</math> is a coupling constant, determining the interaction strength. This model is now known as the '''vector Potts model''' or the '''clock model'''. Potts provided the location in two dimensions of the phase transition for <math>q = 3,4</math>. In the limit <math>q \to \infty</math>, this becomes the [[XY model]].