Quenched disorder and spin-glass correlations in XY nematics

TL;DR

This paper theoretically investigates how quenched disorder affects the ordering and phase transition in 3D XY nematic systems, revealing that disorder becomes irrelevant near the transition point.

Contribution

It applies the replica trick and Gaussian variational method to derive correlation lengths and clarifies the role of disorder near the phase transition in XY nematics.

Findings

Disorder is irrelevant as the order parameter approaches zero.

Correlation length depends on local order and disorder strength.

Disorder does not alter the continuous phase transition.

Abstract

We present a theoretical study of the equilibrium ordering in a 3D XY nematic system with quenched random disorder. Within this model, treated with the replica trick and Gaussian variational method, the correlation length is obtained as a function of the local nematic order parameter and the effective disorder strength. These results clarify what happens in the limiting cases of diminishing order parameter and disorder strength, that is near a phase transition of a pure system. In particular, it is found that quenched disorder is irrelevant as the order parameter tends to zero and hence does not change the character of the continuous XY nematic to isotropic phase transition. We discuss how these results compare with experiments and simulations