Renormalization-group treatment of the dislocation loop model of the smectic-A—nematic transition

A dislocation model for the smectic-$A$—nematic transition is mapped onto a peculiar sort of anistropic superconductor, which is then studied using a momentum-shell renormalization group. The elastic constants behave according to the helium analog, while the specific heat displays an inverted $\lambda$ anomaly. The x-ray correlation-length exponents are ${\nu }_{\parallel }^x\simeq \frac{4}{5}$ and ${\nu }_{\perp }^x\simeq \frac{8}{15}$, in fairly good agreement with experiment.