The Smectic $A$-$C$ Phase Transition in Biaxial Disordered Environments

TL;DR

This paper investigates the continuous phase transition between smectic A and C phases in biaxial disordered environments, revealing a new universality class with calculable critical exponents.

Contribution

It identifies the universality class of both phases as XY Bragg glass and introduces a new universality class for the phase transition using an epsilon expansion.

Findings

Both phases exhibit quasi-long-ranged smectic order.

The phase transition is continuous with a stable fixed point.

Critical exponents are explicitly calculated.

Abstract

We study the smectic $A$-$C$ phase transition in biaxial disordered environments, e.g. fully anisotropic aerogel. We find that both the $A$ and $C$ phases belong to the universality class of the "XY Bragg glass", and therefore have quasi-long-ranged translational smectic order. The phase transition itself belongs to a new universality class, which we study using an $\epsilon=7/2-d$ expansion. We find a stable fixed point, which implies a continuous transition, the critical exponents of which we calculate.