Ordered phase and scaling in Zn models and the three-state antiferromagnetic Potts model in three dimensions

Based on a renormalization-group picture of Z(n) symmetric models in three dimensions, we derive a scaling law for the Z(n) order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective Z(6) symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the renormalization-group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.