Smectic- A and -C phases, and the transition between them, in uniaxial disordered environments

We present a theory of the elasticity and fluctuations of the smectic-A and -C phases in uniaxial, anisotropic disordered environments: e.g., stretched aerogel. We find that, bizarrely, the low-temperature, lower-symmetry smectic-C phase is less translationally ordered than the high-temperature, higher-symmetry smectic-A phase, with short-range “m=1 Bragg glass” and algebraic “XY Bragg glass” order, respectively. The smectic-A–smectic-C (AC) phase transition belongs to a new universality class, whose fixed points and exponents we find in a d=5−ϵ expansion. We give very detailed predictions for the very rich light-scattering behavior of both phases and the critical point.