Devil's staircase, critical thickness, and propagating fingers in antiferroelectric liquid crystals

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.