Abstract
The three-state chiral clock model is studied by means of the Bethe approximation. While the phase diagram obtained by this method resembles the mean-field phase diagram in the vicinity of the boundary to the paramagnetic phase, a significant improvement is achieved in the low and intermediate temperature regions: By a low-temperature expansion of the free energy, which is carried out to third order, we find that, up to this order, the Bethe approximation exactly reproduces the results of the low-temperature analysis of the full model by Yeomans and Fisher. This and the numerical evaluation of the free energy show that, as far as the longer wavelength phases are concerned, the Bethe approximation is in keeping with predictions of Yeomans and Fisher for low temperature, where mean-field theory is qualitatively misleading. At higher temperatures more complicated structures are found to evolve from the basic low-temperature phases by structure combination branching processes in the same fashion as in the phase diagram of the ANNNI model.
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Siegert, M., Everts, H.U. The bethe approximation to the three-state chiral clock model. Z. Physik B - Condensed Matter 66, 227–235 (1987). https://doi.org/10.1007/BF01311659
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DOI: https://doi.org/10.1007/BF01311659