Effect of order parameter fluctuations on the Halperin-Lubensky-Ma first-order transition in superconductors and liquid crystals

We show that order parameter fluctuations in a good type-I superconductor or a liquid crystal always increase the size of the first-order transition. This behavior is eventually changed when the system crosses over to an inverted-XY critical behavior, with the size of the first-order transition vanishing as a power law with a crossover exponent. We find good agreement between our theory and a recent experiment on the nematic-smectic-A first-order transition in 8CB-10CB mixtures of liquid crystals.