Mean-field theory of the three-state chiral clock model

The phase diagram of the three-state chiral clock model, which is known to exhibit commensurate and incommensurate ordered modulated structures, is investigated in the mean-field approximation. First a numerical analysis of the mean-field equations is presented. It is based in the main on the observation that these equations define a non-linear mapping in a four dimensional space. This method of analyzing the mean-field theory proves particularly useful in the determination of the pinning transition of the incommensurate structures. Next the phase diagram is investigated analytically by means of a Landau expansion modified such as to include domain walls. It is found that in the vicinity of the order-disorder transition most features of the phase diagram can be explained quantitatively by this expansion. Finally we present a systematic lowtemperature expansion of the mean-field theory, showing that the low-temperature phase diagram obtained in the mean-field approximation is different from that of the full model.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday