Abstract
The most general quartic Landau free energies are constructed for orientational order parameters which transform like L = 2, 4, and 6 irreducible representations of SO(3). In each case a complete phase diagram is determined using group theoretical techniques in conjunction with the linear programming method. The accessible low-symmetry phases for L = 6 representation are D ∞, Y, O, and D 6. For L = 4 they are D ∞, O, and D 4. D ∞ is accessible for L = 2. In the cases L = 6 and 4 it is found that the phase diagram is dominated by the icosahedral and octahedral symmetries, respectively. The bond densities in the low-symmetry phases are also analyzed.
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