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A functional-integral representation for the partition function of interacting, uniaxial molecules is derived using the Hubbard-Stratonovich transformation. The mean-field evaluation of the partition function gives four possible liquid-crystalline phases (isotropic, nematic, smectic-A, smectic-C) in systems composed of uniaxial molecules. The nature of the multicritical nematic, smectic-A, smectic-C (NAC) point is investigated. Expressions for the parameters that appear in the Landau--de Gennes free energy are derived and the effect of truncating polynomial expansions of the free energy is investigated. It is found that truncation effects can be large.
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Drossinos et al. (1986) studied this question.
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