Abstract
The Ising model and the classical XY model with frustrating second nearest neighbour interaction in an axial direction have qualitatively different properties to each other both at ground state and in the finite temperature. The XY model exposed to the symmetry breaking field with twofold symmetry is here introduced, which is reduced to the Ising model, that is, the ANNNI model in the 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 diagram, while the freedom of XY spin survives only at an area with weak field. This result seems to explain why the successive phase transitions observed in ferro- and antiferro-electric smectic liquid crystals can occur.
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