This construct is related to the m = 5 and m = 6 cases of a Virasoro algebra discrete series representation. A chiral form of it was developed by Rodney Baxter, and the Tutte polynomial is a generalization of the chromatic polynomial that applies to the partition function of this construct. Pauline Hogeweg extended its cellular type, also known as the Glazier/Graner model, to the study of morphogenesis, and its original formulation, known as the clock model, becomes the XY model as q approaches 
This construct is related to the m = 5 and m = 6 cases of a Virasoro algebra discrete series representation. A chiral form of it was developed by Rodney Baxter, and the Tutte polynomial is a generalization of the chromatic polynomial that applies to the partition function of this construct. Pauline Hogeweg extended its cellular type, also known as the Glazier/Graner model, to the study of morphogenesis, and its original formulation, known as the clock model, becomes the XY model as q approaches infinity. Its Hamiltonian is expressed as a summation of Kronecker delta functions of all sites on the lattice. For 10 points, identify this model that is also known as the Ashkin-Teller model and is exactly solvable in one dimension, a model of lattice spins that is a generalization of the Ising Model.
This construct is related to the m = 5 and m = 6 cases of a Virasoro algebra discrete series representation.
Potts model [accept Ashkin-Teller model before it is mentioned]