Effect of density and director fluctuations on the nematic—smectic-Cliquid-crystal transition

When fluctuations of the director and density are taken into account, the second-order nematic—smectic-$C$ transition predicted by mean-field theory is found to become first-order. A dimensionless parameter, which is a measure of the response of director fluctuations to fluctuations in the density, enters the calculation. We investigate the transition for two limiting values of this parameter. In one case we recover the analysis of Swift. In the other we find a transition related to that found by Halperin, Lubensky, and Ma for the nematic—smectic-$A$ transition. We briefly discuss the nature of the director correlation function in the ordered state.