Anisotropic renormalization of thermodynamic quantities above the nematic–smectic-Aphase transition

The results of a self-consistent, one-loop model for the nematic--smectic-A phase transition are presented. Fluctuation-induced renormalization of the correlation lengths parallel and perpendicular to the director and of the twist and bend elastic constants are calculated. The inherently anisotropic nature of the coupling between the director fluctuations and the smectic order parameter directly leads to anisotropic renormalization of the correlation lengths and elastic constants. Because the renormalization of the four quantities mentioned above becomes significant at different temperatures, the crossover from the isotropic high-temperature behavior to the critical, strongly anisotropic behavior is very gradual, producing an extended, weakly anisotropic region, consistent with experimental observations.