Continuous Crystallization in Hexagonally-Ordered Materials

TL;DR

This paper explores the phase transition from liquid crystal to crystalline solid in hexagonally ordered materials, revealing a universality class with critical behavior akin to the XY model and highlighting the influence of elastic properties.

Contribution

It identifies a new universality class for the transition, linking it to the XY model and showing how elastic compliance affects the order of the transition.

Findings

Critical exponents match the XY model.

Elastic compliance influences transition order.

Transition can be continuous or discontinuous.

Abstract

We demonstrate that the phase transition from columnar-hexagonal liquid crystal to hexagonal-crystalline solid falls into an unusual universality class, which in three-dimensional allows for both discontinuous transitions as well as continuous transitions, characterized by a single set of exponents. We show by a renormalization group calculation (to first order in $\epsilon = 4-d$) that the critical exponents of the continuous transition are precisely those of the XY model, which gives rise to a continuous evolution of elastic moduli. Although the fixed points of the present model are found to be identical to the XY model, the elastic compliance to deformations in the plane of hexagonal order, $\mu$, is nonetheless shown to critically influence the crystallization transition, with the continuous transition being driven to first order by fluctuations as the in plane response grows weaker, $\mu \to 0$.