Nematic—to—smectic- A transitions with planar director fluctuations

Nematic---to---smectic-A transitions in liquid crystals with director fluctuations confined to an easy plane are studied via a scaling analysis and an expansion in ε=4-d. The lower critical dimension for these systems is d*=2.5. In three dimensions, scaling predicts anisotropically diverging correlation lengths, with exponents in the ratio 3:2. The ε expansion suggests a fluctuation-driven first-order phase transition for an n-component generalized model, provided $n<110.8$. For $n>110.8$, we find a stable, anisotropic fixed point with, however, a much weaker anisotropy than that predicted by scaling. Two sets of lengths are then necessary to describe order-parameter correlations below the transition. The constraint of planar director fluctuations can, in principle, be imposed experimentally by applying electric fields to nematics with a large transverse dielectric constant. The theory may also be applicable to transitions from smectic-C liquid crystals to bismectics.