Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

We study the three-dimensional generalized six-state clock model at values of the energy parameters at which the system is considered to have the same behavior as the stacked triangular antiferromagnetic Ising model and the three-state antiferromagnetic Potts model. First, we investigate ordered phases by using the Monte Carlo twist method (MCTM). We confirmed the existence of an incompletely ordered phase (IOP1) at intermediate temperature, besides the completely ordered phase at low temperature. In this intermediate phase, two neighboring states of the six-state model mix, while one of them is selected in the low-temperature phase. We examine the fluctuation the mixing rate of the two states in IOP1 and clarify that the mixing rate is very stable around 1:1. The high-temperature phase transition is investigated by using a nonequilibrium relaxation method. We estimate the critical exponents beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY universality class. The low temperature phase transition is found to be of first-order by using MCTM and finite-size-scaling analyses.