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The superconducting phase transition is predicted to be weakly first order, because of effects of the intrinsic fluctuating magnetic field, according to a Wilson-Fisher -expansion analysis, as well as a generalized mean-field calculation appropriate to a type-I superconductor. Similar results hold for the phase transition from a smectic-A to a nematic liquid crystal.
Halperin et al. (Mon,) studied this question.