Abstract
In the ferro- and antiferro-electric smectic liquid crystals the molecules tilt in a helical plane, whose state are expressed in terms of the Ising spin, though the molecules could be expressed by the XY model. The Ising model and the classical XY model with frustrating seocnd nearest neighbour interaction in an axial direction are known to have different properties to each other even quahtatively. The XY model exposed to the symmetry breaking field with twofold symmetry is introduced here, which is reduced to the Ising model, that is, the ANNNI model in a limit of the strong field strength. The ground state of this model is examined, in which the freedom of the XY spin is shown to be suppressed at rather small strength of the symmetry breaking field and accordingly the Ising properties dominate in large area on an interaction parameter versus field cliagram, while XY-like freedom survives only at an area with weak field. This result seems to explain why the successive phase transitions observed in ferro- and antiferro-electric smectics can occur.
