Abstract
Axial next nearest neighbour XY model with biquadratic interaction is studied to elucidate a behaviour of the direction of molecular tilt in the phenomena of successive phase transitions of antiferroelectric smectics. The ordered phase with a symmetry of the XY model appears from a disordered one, and at the low temperature region the transition from that phase to the one with the Ising symmetry occurs discontinuously, which differs slightly from the crossover behaviour occurring at the similar system with two-fold field in place of the biquadratic interaction where the phase with Ising symmetry appears at the critical line.
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