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We show that order-parameter fluctuations in a good type-I superconductor ora liquid crystal always increase the size of the first-order transition. Thisbehavior is eventually changed when the system crosses over to inverted-XYcritical behavior, with the size of the first-order transition vanishing as apower law with a crossover exponent. We find a good agreement between ourtheory and a recent experiment on the nematic-smectic-A first-order transitionin 8CB-10CB mixtures of liquid crystals.Comment: 4 pages, RevTex, 2 postscript figures include

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