Nematics with quenched disorder : violation of self-averaging

TL;DR

This paper investigates how quenched disorder in aerogel affects the isotropic-to-nematic transition in liquid crystals, revealing severe violations of self-averaging that can eliminate phase transitions in certain cases.

Contribution

It demonstrates the extent to which quenched disorder causes violation of self-averaging in liquid crystal phase transitions, including conditions where phase transitions disappear.

Findings

Severe violation of self-averaging in weakly first-order transitions.

Non-self-averaging correlation length in certain conditions.

Persistence of phase transition in more strongly first-order cases.

Abstract

We consider the isotropic-to-nematic transition in liquid crystals confined to aerogel hosts, and assume that the aerogel acts as a random field. We generally find that self-averaging is violated. For a bulk transition that is weakly first-order, the violation of self-averaging is so severe, even the correlation length becomes non-self-averaging: no phase transition remains in this case. For a bulk transition that is more strongly first-order, the violation of self-averaging is milder, and a phase transition is observed.