Devil's Staircase, Critical Thickness, and Propagating Fingers in Antiferroelectric Liquid Crystals

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From an expression for the energy of a cell containing an antiferroelectric smectic liquid crystal with only nearest-neighbor interactions between layers we conclude the following: (1) a critical cell thickness exists at which the commensurability of the system changes from unity to higher values; (2) for negative dielectric anisotropy there is another critical thickness below which a transition to ferroelectric alignment cannot be homogeneously nucleated at any field; and (3) the transition to and from ferroelectric alignment propagates as a stable solitary wave under certain conditions.