Elastic Fluctuations can drive Ferroelectric Transitions Incommensurate

We consider a Ginzburg-Landau theory for a ferroelectric phase transition whose primary order parameter (electrical polarization) is coupled to elastic strain through electrostriction. We show that the strain coupling leads to a quartic term in the effective Hamiltonian that describes long-range, anisotropic interactions between fluctuations in the order parameter. At the level of mean field theory plus Gaussian fluctuations, we demonstrate that the ferroelectric instability is driven to a finite wavevector, so that the transition from the disordered phase to the fully ordered ferroelectric phase must occur via an incommensurate phase.