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In the present paper a discrete mean-field model for thin smectic A liquid crystal films with two boundary surfaces is offered. The model accounts for the recently observed phenomenon of layer-thinning transitions in free-standing smectic A films upon heating. In particular, the model predicts the observed multiple layer jumps, as well as, for films thinner than 13 layers, the observed power law dependence of the layer-thinning transition temperatures on film thickness.
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