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

Abstract

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