A Landau-Ginzburg free energy is presented that yields a nematic to smectic-A (NA) transition, a nematic to smectic-C (NC) transition, and a Lifshitz point (at the boundary between the NA and NC transitions). Fluctuation enhancements of the Frank elastic constants are calculated. For the NC transition, all three elastic constants K₁, K₂, and K₃ diverge as ξ², where ξ is the correlation length for fluctuations of the smectic order parameter. At the Lifshitz point, K₁ and K₂ diverge as lnξ whereas K₃ diverges as ξ.
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Chen et al. (1976) studied this question.
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