  We study a square-lattice three-state Potts antiferromagnet with a staggered
polarization field at finite temperature. Numerically treating the transfer
matrices, we determine two phase boundaries separating the model-parameter
space into three parts. We confirm that one of them belongs to the
ferromagnetic three-state Potts criticality, which is in accord with a recent
prediction, and another to the Ising type; these are both corresponding to the
massless renormalization-group flows stemming from the Gaussian fixed points.
We also discuss a field theory to describe the latter Ising transition.
