For the clock model, there is evidence that the corresponding phase transitions are infinite order BKT transitions, and a continuous phase transition is observed when q ≤ ≤ 4 . Further use is found through the model's relation to percolation problems and the Tutte and chromatic polynomials found in combinatorics. For integer values of q ≥ ≥ 3 , the model displays the phenomenon of 'interfacial adsorption' with intriguing critical wetting properties when fixing opposite boundaries in two different states .