Enhanced Long Wavelength Mermin-Wagner Fluctuations in Active Crystals and Glasses

TL;DR

This paper explores how active forces in 2D and 3D systems amplify long-wavelength fluctuations, modifying the critical dimension and causing a logarithmic divergence in particle displacement, revealing new non-equilibrium behaviors.

Contribution

It demonstrates that active forces can significantly enhance Mermin-Wagner fluctuations, changing the critical dimension and inducing divergence in 3D systems.

Findings

Active forces couple with density fluctuations, altering critical dimensions.

Logarithmic divergence of MSD in 3D due to active fluctuations.

Fluctuations are stronger in active glassy and crystalline systems.

Abstract

In two-dimensions (2D), the Mermin-Wagner-Hohenberg (MWH) fluctuation plays a significant role, giving rise to striking dimensionality effects marked by long-range density fluctuations leading to the singularities of various dynamical properties. According to the MWH theorem, a 2D equilibrium system with continuous degrees of freedom cannot achieve long-range crystalline order at non-zero temperatures. Recently, MWH fluctuations have been observed in glass-forming liquids, evidenced by the logarithmic divergence in the plateau value of mean squared displacement (MSD). Our research investigates long-wavelength fluctuations in crystalline and glassy systems influenced by non-equilibrium active noises. Active systems serve as a minimal model for understanding diverse non-equilibrium dynamics, such as those in biological systems and self-propelled colloids. We demonstrate that fluctuations from active forces can strongly couple with long-wavelength density fluctuations, altering the lower critical dimension ($d_l$) from $2$ to $3$ and leading to a novel logarithmic divergence of the MSD plateau with system size in 3D.