Successive Phase Transitions in Antiferroelectric Liquid Crystal Systems
  An axial next-nearest-neighbor XY model is studied as a model of chiral liquid crystals which exhibit many ferro-, ferri- and antiferroelectric tilted smectic phases. Depending on the values of interaction parameters, this model exhibits Ising symmetric (i.e., the tilt directions of directors are parallel or anti parallel) phases or XY symmetric phases. Phases with each type-of-symmetry show the character of devil's staircase, which has been observed in experiments. 
Masaya Koroishi, Masashi Torikai and Mamoru Yamashita