Relative chirality of octupolar columns in a triangular array

The relative chirality of helical columns of planar disks having threefold symmetry is studied using a model Hamiltonian derived from symmetry arguments that describe low-order octupole interactions. The columns are assumed to pack in a triangular array perpendicular to the columnar axes. Ground-state and finite-temperature mean-field phase diagrams are obtained as functions of interaction parameters. Due to the structure of the disks, there appears a term in the Hamiltonian that is not present for systems with lower internal symmetry, such as classical spin systems. This interaction is responsible for the stabilization of phases in which one third of the columns have a chirality opposite to the others. Such a phase has been observed in the discotic liquid crystal hexa-hexylthiotriphenylene.