Lattice models and Landau theory for type-II incommensurate crystals

Ground-state properties and phonon dispersion curves of a classical linear-chain model describing a crystal with an incommensurate phase are studied. This model is the DIFFOUR (discrete frustrated phi(4)) model with an extra fourth-order term added to it. The incommensurability in these models may arise if there is frustration between nearest-neighbor and next-nearest-neighbor interactions. We discuss the effect of the additional term on the phonon branches and phase diagram of the DIFFOUR model. We fmd some features not present in the DIFFOUR model such as the renormalization of the nearest;neighbor coupling. Furthermore, the ratio between the slopes of the soft phonon mode in the ferroelectric and paraelectric phase can take on values different from -2. Temperature dependences of the parameters in. the model are different above and below the paraelectric transition, in contrast with the assumptions made in Landau theory.,In the continuum limit this model reduces to the Landau-free-energy expansion for type-II incommensurate crystals and it can be seen as the lowest-order generalization of the simplest Lifshitz-point model. Part of the numerical calculations have been done by an adaption of the effective potential method, originally used for models with nearest-neighbor interaction, to models with also next-nearest-neighbor interactions.