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We propose the Landau model for lock-in phase transitions in uniaxiallymodulated improper ferroelectric incommensurate-commensurate systems of classI. It includes Umklapp terms of third and fourth order and secondary orderparameter representing the local polarization. The corresponding phase diagramhas the structure of harmless staircase, with the allowed wave numbers obeyingthe Farey tree algorithm. Among the stable commensurate phases only those withperiods equal to odd number of lattice constants have finite macroscopicpolarizations. These results are in excellent agreement with experimentalfindings in some A2BX4 compounds.Comment: 9 pages, 5 figures, revtex, to be published in Journal of Physics:  Cond. Matter as a Letter to the Edito

Landau model for commensurate-commensurate phase transitions in uniaxial improper ferroelectric crystals