Anomalous elasticity of nematic elastomers

TL;DR

This paper investigates the scale-dependent elastic properties of nematic elastomers using renormalized field theory, revealing anomalous moduli behavior that varies with length scale, especially around the critical dimension of 3.

Contribution

It introduces a minimal Landau-Ginzburg-Wilson elastic energy model and analyzes fluctuation effects, uncovering scale-dependent anomalies in elastic moduli.

Findings

Certain elastic moduli depend on length scale in a logarithmic or power-law manner.

One shear modulus vanishes at large scales.

The bending modulus diverges at long length scales.

Abstract

We study the anomalous elasticity of nematic elastomers by employing the powers of renormalized field theory. Using general arguments of symmetry and relevance, we introduce a minimal Landau-Ginzburg-Wilson elastic energy for nematic elastomers. Performing a diagrammatic low temperature expansion, we analyze the fluctuations of the displacement fields at and below the upper critical dimension 3. Our analysis reveals an anomaly of certain elastic moduli in the sense that they depend on the length scale. In $d = 3$ this dependence is logarithmic and below $d=3$ it is of power law type with anomalous scaling exponents. One of the 4 relevant shear moduli vanishes at long length scales whereas the only relevant bending modulus diverges.