Applications of Larkin-Khmelnitzkii theory to static and dynamical critical phenomena in uniaxial ferroelectrics

The logarithmic correction factors to classical Landau theory due to order parameter fluctuations close to the Curie point are used to calculate various static and dynamic properties for small t ≡ |T — Tc|/Tc. The specific heat at constant polarization has below Tc a cusp ∞ |log t|-2/3. The leading term in the spin-lattice relaxation rate 1/Tt, varies as log t just as in classical theory and in agreement with experiment in colemanite. The damping of low-frequency longitudinal sound waves propagating perpendicular to the easy axis varies as t-1|logt|2/3 below Tc (relaxation damping) and as t-1|log t|-1/3 above Tc (fluctuation damping); the ratio of these two terms is material independent, analogously to recent experiments at the superfluid phase transition in helium II. Propagation of sound not perpendicular to the polar axis suppresses the damping due to the relaxation of the long-range order parameter and leaves only the fluctuation damping. The energy of 180° domain walls vanishes as t3/2|log t|1/2 whereas the domain width, just as in classical theory, remains constant. Earlier estimates of the size of the critical region (“Ginzburg criterion”) in triglycine sulfate are criticized.