We have studied the frustration between ferro- and antiferro-electricity in chiral smectic C like liquid crystalline phases, which is not only fundamentally interesting but also very attractive from an application point of view. It causes temperature induced successive phase transitions as characterized by a devil's staircase and the thresholdless, hysteresis-free, V-shaped switching induced by an applied electric field. The devil's staircase indicates some type of interlayer ordering, while the V-shaped switching suggests considerably diminished tilting correlation. These two are apparently contradictory to each other, but result from the same cause, i.e. the frustration. We have first summarized experimental facts regarding subphases and successive phase transitions observed in many compounds and mixtures, which we believe are related to one another and result from the frustration. We have introduced several different theoretical explanations for these observed facts, and shown that only the axial next nearest neighbor Ising (ANNNI) model can explain almost all of the facts, provided that it is unified with the XY model appropriately. The unified model can make a comprehensive explanation in the most natural way based on the most probable molecular interactions. We have then emphasised that there are several modes regarding the V-shaped switching, because the system becomes so soft with respect to the tilting direction and sense that any additional external or internal force modifies the in-plane local director alignments. For the practically usable ones, we have emphasised the need for some type of randomization in the molecular alignment at the tip of the V and/or the switching process. In particular, the two dimensional (ideally, cylindrically symmetric) azimuthal angle distribution of local in-plane directors around the smectic layer normal is most attractive. Such a randomized state at the tip of the V is thermodynamically unique under a given condition imposed by interfaces. It stays stable even when the smectic layer structure, such as a chevron, changes with temperature. Finally, we have summarized the so-far reported compounds and mixtures for the V-shaped switching and introduced some prototypes of LCDs using them.
A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree