Haldar Astik, Sarkar Apurba, Chatterjee Swarnajit, Basu Abhik
Theory Division, Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute, 1/AF Bidhannagar, Calcutta 700064, West Bengal, India.
School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata-700032, West Bengal, India.
Phys Rev E. 2023 Sep;108(3-1):034114. doi: 10.1103/PhysRevE.108.034114.
We explore the generic long-wavelength properties of an active XY model on a substrate, consisting of a collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation, and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it displays generalized quasi-long-range order (QLRO): It shows phase ordering which is generically either logarithmically stronger than the conventional QLRO found in its equilibrium limit, together with "miniscule number fluctuations," or logarithmically weaker than QLRO along with "giant number fluctuations," showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short-range phase order are found, characterized by the presence or absence of stable clusters of finite sizes. In a surprising connection, the hydrodynamic theory for this model also describes the fluctuations in a Kardar-Parisi-Zhang (KPZ) surface with a conserved species on it, or an active fluid membrane with a finite tension, without momentum conservation and a conserved species living on it. This implies the existence of stable fluctuating surfaces that are only logarithmically smoother or rougher than the Edward-Wilkinson surface at two dimensions (2D) can exist, in contrast to the 2D pure KPZ-like "rough" surfaces.
我们研究了基底上活性XY模型的一般长波特性，该模型由一组与扩散的守恒物种接触的近相位有序活性XY自旋组成，作为具有守恒定律的活性自旋体的一个代表性系统。自旋在固体基底上响应局部密度涨落和局部相位差而主动旋转。我们通过基于代理模型的蒙特卡罗模拟来研究这个系统，并辅以该系统的流体动力学理论。我们证明，该系统可以在没有任何流体动力学相互作用的情况下实现相位同步。我们的数值和分析相结合的研究表明，这个模型在稳定时表现出迄今未被研究的标度行为：由于迁移率、主动旋转和数量守恒之间的相互作用，这样一个系统在以相位和密度涨落之间的新颖对应关系为特征的广泛模型参数范围内可以是稳定的。在相位有序系统稳定的相空间的不同区域，它表现出广义准长程有序（QLRO）：它表现出的相位有序通常比在其平衡极限中发现的传统QLRO强对数倍，同时伴有“微小的数量涨落”，或者比QLRO弱对数倍，同时伴有“巨大的数量涨落”，在有序状态下显示出相位有序和密度涨落之间的新颖一一对应关系。有趣的是，发现这些标度指数明确依赖于模型参数。我们进一步表明，在其他参数区域中不存在稳定的有序相。相反，发现了两种具有短程相位有序的不同类型的无序状态，其特征是存在或不存在有限大小的稳定团簇。令人惊讶的是，这个模型的流体动力学理论还描述了其上有守恒物种的 Kardar-Parisi-Zhang（KPZ）表面或具有有限张力、没有动量守恒且其上有守恒物种的活性流体膜中的涨落。这意味着存在仅比二维（2D）的 Edward-Wilkinson 表面对数上更光滑或更粗糙的稳定涨落表面，这与二维纯 KPZ 类的“粗糙”表面形成对比。
