It is shown that mean-field theory fails to give a correct qualitative picture of the thermodynamic behavior of the q-state Potts model when the exchange interaction is anisotropic in spin space. The correct picture is recovered either by introducing a single-particle anisotropy or by taking correlations into account via a Bethe-Peierls approximation. This analysis helps the interpretation of previous renormalization-group results for asymmetric Potts models
