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Static and dynamic critical behavior of Sn$_2$P$_2$S$_6$ type ferroelectricsand (Pb$_y$Sn$_{1-y}$)$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ mixed crystals with lineof tricritical points and line of Lifshitz points on the $T-x-y$ phase diagram,which meet at the tricritical Lifshitz point, can be described in a combinedBEG-ANNNI model. Such the model considers first and second neighborinteractions for pseudospins in a local three-well potential. Below thetemperature of tricritical Lifshitz point, the "chaotic" state accompanied bythe coexistence of ferroelectric, metastable paraelectric and modulated phasesis expected. In addition to the frustration of polar fluctuations near theBrillouin zone center, in Sn$_2$P$_2$S$_6$ crystal the antipolar fluctuationsalso strongly develop in the paraelectric phase at cooling to continuous phasetransition temperature $T_0$. Here, critical behavior can be described as acrossover between Ising and XY universality classes, what is expected nearbicritical points with coupled polar and antipolar order parameters andcompeting instabilities in $q$-space.

Phase diagram of ferroelectrics with tricritical and Lifshitz points at coupling between polar and antipolar fluctuations