Incompletely ordered phase in the three-dimensional six-state clock model: Evidence for an absence of ordered phases of XY character

By employing our interfacial method, which uses Monte Carlo simulations, we show in various ways that the three-dimensional six-state clock model has an incompletely ordered phase (IOP) due to entropy gains where two nearest clock-spin states are dominant with equal weight. Our obtained results strongly imply its equivalence with the three-state antiferromagnetic Potts model, confirming the absence of ordered phases of XY character and the existence of a different universality class for the upper phase transition of the IOP. The disordered flat phase recently found in the restricted solid-on-solid model is pointed out to be an IOP.