An analogy between superconductors and smectics A

The conformation of a smectic A can be described by a phase function φ( R), the n-th layer corresponding to φ( R) = 2 πn. The role of the phase in smectics A and in superfluids is similar. This analogy leads to the following predictions for a second order smectic A↔ nematic transition: (1) the transition temperature is lowered if twist, or bend distortions are imposed: these distortions correspond to a magnetic field in superconductors. (2) the Frank coefficients K₂ and K₃ of the nematic phase must show pretransitional anomalies.