AI 中文总结
该研究推导并分析手性伊辛模型的平均场理论，揭示手性偏置导致畴各向异性粗化与粗化停滞，还发现手性指状不稳定性，为手性活性物质研究提供理论基础。
AI 中文摘要
我们推导并分析了由Wang、Pietzonka和Jülicher在《Edge Currents Shape Condensates in Chiral Active Matter》（arXiv:2603.20064）中提出的手性伊辛模型的平均场理论。从2×2自旋块顺时针和逆时针旋转的主方程出发，我们首先得到空间分辨平均磁化强度的空间离散演化方程。在该离散层面，我们表明手性偏置强烈影响相粗化：畴各向异性粗化，形成近矩形形状，最终呈现手性诱导的粗化停滞。对这些方程取连续极限得到活性场论，其结构为松弛型Model-B类动力学，辅以手性电流，使系统永久远离平衡态。粗粒化明确显示微观旋转偏置如何在界面处产生切向电流。利用该连续理论，我们对径向对称团簇进行线性稳定性分析，识别出手性指状不稳定性，其中界面的角向扰动被放大，最终导致径向不对称旋转态或无序态。
英文摘要
We derive and analyze a mean-field theory of the chiral Ising model recently introduced by Wang, Pietzonka, and Jülicher in "Edge Currents Shape Condensates in Chiral Active Matter", arXiv:2603.20064. Starting from the master equation for clockwise and counterclockwise rotations of 2x2 spin blocks, we first obtain spatially discrete evolution equations for the spatially resolved average magnetization. On this discrete level, we show that a chiral bias strongly affects phase coarsening: domains coarsen anisotropically, develop nearly rectangular shapes, and eventually display chirality-induced arrested coarsening. Taking the continuum limit of these equations yields an active field theory that has the structure of a relaxational Model-B-type dynamics supplemented by a chiral current that permanently drives the system out of equilibrium. The coarse graining explicitly shows how microscopic rotational bias generates tangential currents localized at interfaces. Using this continuum theory, we perform a linear stability analysis of radially symmetric clusters and identify a chiral fingering instability in which angular perturbations of the interface are amplified and eventually lead to radially asymmetric rotating states or disordered states.
