Dirty, Skewed, and Backwards: The Smectic A-C Phase Transition in Aerogel

We study the smectic A-C transition in anisotropic and uniaxial disordered environments, e.g., uniaxially stretched aerogel. We find very strange behavior of translational correlations: the low-temperature, lower-symmetry smectic C phase is less translationally ordered than the high-temperature, higher-symmetry smectic A phase, with short ranged and algebraic translational correlations, respectively. Specifically, the A and C phases belong to the quasi-long-ranged translationally ordered “XY Bragg glass” and short ranged translationally ordered “m=1 Bragg glass” phase, respectively. The A-C phase transition itself belongs to a new universality class, whose fixed points and exponents we find in a d=5-ϵ expansion.