Abstract
Free-standing liquid crystal films with positive diamagnetic susceptibility can have the smectic ordering enhanced by an external field applied perpendicular to the plane layers. Within a quadratic functional integral approach, we investigate the interplay between the smectic order induced by an external field H and that due to the surface tension γ between the film and the surrounding gas. We find that the average smectic fluctuation is a non-monotonic function of film thickness, with a characteristic thickness scale ξH delimiting the predominance of surface tension and magnetic field effects. This characteristic thickness obeys simple asymptotic power-law relations as a function of the ordering terms which allows us to represent the average smectic fluctuations in a universal scaling form.
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