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Ground state properties and phonon dispersion curves of a classical linearchain model describing a crystal with an incommensurate phase are studied. Thismodel is the DIFFOUR (discrete frustrated phi4) model with an extrafourth-order term added to it. The incommensurability in these models may ariseif there is frustration between nearest-neighbor and next-nearest-neighborinteractions. We discuss the effect of the additional term on the phononbranches and phase diagram of the DIFFOUR model. We find some features notpresent in the DIFFOUR model such as the renormalization of thenearest-neighbor coupling. Furthermore the ratio between the slopes of the softphonon mode in the ferroelectric and paraelectric phase can take on valuesdifferent from -2. Temperature dependences of the parameters in the model aredifferent above and below the paraelectric transition, in contrast with theassumptions made in Landau theory. In the continuum limit this model reduces tothe Landau free energy expansion for type II incommensurate crystals and it canbe seen as the lowest-order generalization of the simplest Lifshitz-pointmodel. Part of the numerical calculations have been done by an adaption of theEffective Potential Method, orginally used for models with nearest-neighborinteraction, to models with also next-nearest-neighbor interactions.Comment: 33 pages, 7 figures, RevTex, submitted to Phys. Rev.

Lattice models and Landau theory for type-II incommensurate crystals