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<p>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 (<i>d</i><sub><i>l</i></sub>) from 2 to 3 and leading to a novel logarithmic divergence of the MSD plateau with system size in 3D.</p>

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Enhanced long wavelength Mermin-Wagner-Hohenberg fluctuations in active crystals and glasses

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月1日

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  • Subhodeep Dey,
  • Antik Bhattacharya,
  • Smarajit Karmakar

摘要

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 (dl) from 2 to 3 and leading to a novel logarithmic divergence of the MSD plateau with system size in 3D.