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Lattice model for layered structures.

We present and investigate a lattice model for layered structures. It involves a lattice Laplacian operator and corresponds to a three-dimensional XY model with competing antiferromagnetic nearest- and ferromagnetic next- and third-nearest-neighbor couplings. The model describes the loss of order in a wide variety of layered systems, most notably the layered phases of microemulsions and smectic liquid crystals, where the transition leads to an isotropic or a nematic phase with a residual orientational order. The latter point is demonstrated by integrating out the nematic order fluctuations in a much more general model also proposed in this article, which extends the de Gennes field theory by describing the transitions between isotropic, nematic, and smetic-A phases of liquid crystals. Monte Carlo simulations exhibit a first-order isotropic-layered phase transition, changing to second order in the limit of infinite interlayer distance.