大自旋波涨落抑制马尔萨斯鸟群的活动
Large Spin-Wave Fluctuations Suppress Activity in Malthusian Flocks
AI总结：
本文研究二维马尔萨斯鸟群，发现其存在等价于平衡态XY模型的新奇相，识别出由活性与自旋波相互作用导致的新奇临界点，该系统在强噪声下会过渡到平衡态XY普适类。
AI中文摘要：
二维鸟群模型中，除长程有序外的新奇相仍在不断被发现，使鸟群成为活性物质领域的关键范式之一。然而，围绕马尔萨斯（恒定密度）鸟群（比Vicsek模型更易解析的替代模型）的讨论，大多集中在星体增殖前中间区域的标度指数上，留下了该模型可能呈现哪些其他相的问题。本文研究二维马尔萨斯鸟群的动力学，识别出一种此前未被注意到的相，其动力学等价于平衡态XY模型。通过确定模型的对称性，推导戈德斯通模式的有效运动方程并分析自旋波涨落；识别出区分两个不同相的新奇临界点，采用微扰重整化群（RG）方法确定其附近的RG流，进而计算该临界点的普适标度行为及其对数修正。与平衡态对应物（在涡旋等有效自由度上发生相变）不同，本文的新奇相变源于活性与自旋波的相互作用。不过，其RG流与Berezinskii-Kosterlitz-Thouless（BKT）相变的RG流相似，且研究表明，对于足够强的噪声，活性变得无关紧要，系统会过渡到平衡态XY普适类。
英文摘要：
Novel phases, beyond long-range order in two dimensions, have continued to be discovered within flocking models, establishing flocking as one of the pivotal paradigms in active matter. However, much of the discussion around ``Malthusian'' (constant density) flocks, an analytically more tractable alternative to the Vicsek model, has centred around the scaling exponents governing the intermediate regime prior to the proliferation of asters, leaving open the question of what other phases the model might display. Here, we study the two-dimensional dynamics of Malthusian flocks and identify a previously unnoticed phase, where the dynamics is that of the equilibrium XY Model. By identifying the symmetries of the model, we derive the effective equations of motion for the Goldstone modes and analyse the spin-wave fluctuations. We identify a novel critical point separating two distinct phases and, using a perturbative RG procedure, determine the RG flows in its vicinity. This allows us to calculate the universal scaling behaviour at the critical point, along with its logarithmic corrections. The novel phase transition here is due to the interaction of activity and spin-waves, unlike the equilibrium counterpart, which undergoes a phase transition in effective degrees of freedom, namely vortices. Nevertheless, the RG flows are similar to those of the Berezinskii-Kosterlitz-Thouless transition, and we show that for sufficiently strong noise, the activity becomes irrelevant and the system crosses over to the equilibrium XY universality class.
