Fluctuations and Landau—Devonshire expansion for barium titanate

The experimentally observed temperature dependence of the quartic coefficients in the Landau—Devonshire expansion for BaTiO$_3$ is naturally accounted for within a proper fluctuation model. It is explained, in particular, why one of the quartic coefficients varies with temperature above $T_c$ while the second is constant. The tetragonal phase in BaTiO$_3$ is argued to exist essentially due to the thermal fluctuations, while the true Landau—Devonshire expansion with temperature-independent coefficients favours the rhombohedral ferroelectric phase.