  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.
