Theory of theSA1−SA2phase transition in liquid crystals

We present a phenomenological model for the phase transition between the monolayer ($S_{A_1}$) and the bilayer ($S_{A_2}$) phases of smectic liquid crystals. This model contains all relevant symmetries and Goldstone modes. We study the transition using the $\epsilon$ expansion and find it to be in the same universality class as the Ising model to first order in $\epsilon$. In three dimensions, the physical correlation function, however, exhibits nonuniversal power-law behavior leading to a nonuniversal susceptibility exponent $\gamma$.