Smectics $A$ and $C$, and the Transition between them, in Uniaxial Disordered Environments

TL;DR

This paper develops a theoretical framework for understanding the elasticity and fluctuations of Smectic A and C phases in uniaxial disordered environments, revealing unexpected ordering properties and a new universality class for the phase transition.

Contribution

It introduces a novel theory describing the elastic and fluctuation behavior of Smectic A and C phases in disordered environments, identifying a new universality class for the phase transition.

Findings

Smectic C phase is less translationally ordered than Smectic A.

The phase transition belongs to a new universality class.

Detailed predictions for light scattering behavior.

Abstract

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-ranged "$m=1$ Bragg glass" and algebraic "XY Bragg glass" order, respectively. The $AC$ phase transition belongs to a new universality class, whose fixed points and exponents we find in a $d=5-\epsilon$ expansion. We give very detailed predictions for the very rich light scattering behavior of both phases, and the critical point.