标题： 缺陷介导的聚集和运动诱导的相分离在活性XY模型中 显示英文标题

标题： Defect-Mediated Aggregation and Motility-Induced Phase Separation in Active XY Model

摘要： 我们提出了一种“主动XY模型”，该模型结合了经典XY模型和Vicsek模型的关键要素，以研究拓扑缺陷在活性物质系统中的作用。 该模型具有XY自旋自由度的自推进粒子，并引入了一个控制粒子运动方向偏差的自推进参数。 通过数值模拟，我们证明自推进会引发运动诱导的相分离（MIPS），其中粒子聚集在具有正涡旋电荷的拓扑缺陷周围。 相反，负电荷缺陷则倾向于消散。 我们分析了这些聚类的演化，并表明它们的增长遵循两阶段的指数弛豫过程，特征时间与系统大小$L$成$\tau \sim L^{3}$的比例，类似于平衡系统中的第一类相分离。 我们的结果突显了拓扑缺陷在活性系统中相分离和聚类行为中的重要作用，连接了非平衡动力学与平衡理论。 显示英文摘要

摘要： We propose an ``active XY model'' that incorporates key elements of both the classical XY model and the Vicsek model to study the role of topological defects in active matter systems. This model features self-propelled particles with XY spin degrees of freedom on a lattice and introduces a self-propulsion parameter controlling the directional bias of particle motion. Using numerical simulations, we demonstrate that self-propulsion induces motility-induced phase separation (MIPS), where particles aggregate into clusters around topological defects with positive vortex charge. In contrast, negative charge defects tend to dissipate. We analyze the evolution of these clusters and show that their growth follows a two-stage exponential relaxation process, with characteristic time scaling as $\tau \sim L^{3}$ with the system size $L$, reminiscent of first-order phase separation in equilibrium systems. Our results highlight the important role of topological defects in phase separations and clustering behavior in active systems, bridging nonequilibrium dynamics and equilibrium theory.