On the Landau theory of phase transitions: a hierarchical dynamic model

The Landau theory of phase transitions has been re-examined under the framework of a modified mean field theory in ferroelectrics. By doing so, one can see that there are two atomic movements involved in the ferroelectric phase transition; the first corresponds to the vibration of the crystalline lattice, which will render phonon mode softening at the critical point, and the second represents the slow evolution of a partially ordered nematic phase formed by the cooperative behavior of high-temperature structure precursors. In this hierarchical dynamic structure, the former fast dynamics could be significantly modulated by the latter slow dynamics in the vicinity of the Curie temperature; it then turns out that it is the behavior of the nematic phase on approaching the critical point that makes the Landau theory deviate from experimental observations.