Exponential Decay of Correlations in a Model for Strongly Disordered 2D Nematic Elastomers

TL;DR

This study uses Monte Carlo simulations to show that in a 2D nematic system with strong disorder, correlations decay exponentially, revealing a new behavior different from previous theoretical predictions.

Contribution

The paper demonstrates, through simulations, a novel exponential decay of correlations in disordered 2D nematic systems, contrasting with earlier Gaussian or power-law models.

Findings

Correlation length decays exponentially with disorder strength

Long-range correlations decay exponentially in strong disorder

Results differ from Gaussian and power-law decay predictions

Abstract

Lattice Monte-Carlo simulations were performed to study the equilibrium ordering in a two-dimensional nematic system with quenched random disorder. When the disordering field, which competes against the aligning effect of the Frank elasticity, is sufficiently strong, the long-range correlation of the director orientation is found to decay as a simple exponential, Exp[-r/x]. The correlation length {x} itself also decays exponentially with increasing strength of the disordering field. This result represents a new type of behavior, distinct from the Gaussian and power-law decays predicted by some theories.