Abstract
A one-dimensional Hamiltonian is derived upon microscopic considerations to model the columnar phases of a liquid crystal made of molecules of discrete rotational symmetry. The study deals with the ground state of this Hamiltonian, only the orientational degrees of freedom being taken into account. The intracolumnar interaction is described by the natural cantedness of an isolated column, while interaction parameters H and G characterize the amplitude of the local crystal field at a site originating from the other surrounding columns. The phase diagrams of the orientational ordering along the column are numerically investigated and a previous analytical approach is briefly recalled. A new perturbation development is proposed. This allows us to analyse a multiphase point and to explain the appearance of an infinity of phases in the vicinity of this point. The anisotropy of the columnar lattice is then investigated with the use of the same perturbation development, and some of the properties of a complex phase diagram are examined numerically as well as analytically.
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