The phase diagram of the mean-field transfer-matrix (MFTM) approximation for the three-dimensional p-state chiral clock model is determined numerically for p=3, 4, and 5 and compared to the simple mean-field and exact low-temperature phase diagrams. The MFTM approximation is a natural extension of mean-field theory in which the interactions are treated exactly in one direction with mean-field treatment of the other directions. For p=3, the MFTM low-temperature phase sequence near the multiphase point agrees with the exact low-temperature phase diagram, which is different from that of the simple mean-field theory. Thus, treating only the direction of anisotropy exactly in the three-state chiral clock model results in an improvement over simple mean-field theory in the qualitative (as well as the quantitative) features of the phase diagram. The case p=4 is similar, but for p=5 the MFTM approximation is inconclusive in a way that suggests a change in the nature of the model for p≥5. The results indicate that with care the MFTM method is useful for analyzing the qualitative phase behavior of models with modulated phases.

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