标题： 布朗运动$q=2$ Potts 模型的数值研究 显示英文标题

标题： Numerical investigation of the Brownian $q=2$ Potts Model

摘要： 在活性物质中，例如群体运动的Vicsek模型，粒子具有内部自由度，比如它们的方向向量，只要其他粒子在其一定范围内，就会受到相互作用的影响。 为了更好地理解空间自由度与内部自由度之间的相互作用，我们数值研究了离散格点上和非格点上的 $q=2$ 模型的一个变体，其中粒子还受到布朗运动的影响。 内部自由度对空间自由度缺乏反馈使得该模型本质上是非平衡态的。 我们证实了之前的研究结果，即相变的静态指数不受扩散的影响。 与之前的工作不同，我们表明有序聚集体的形成不会因扩散而被破坏，而应被视为一种有效的相互作用形式。 我们展示了如何基于著名的A、B和C模型来理解我们的数值发现：在非格点上，布朗运动的 $q=2$ 模型是C模型；在格点上，它是A模型，并带有额外的（无关且守恒的）B模型噪声。 显示英文摘要

摘要： In active matter, such as the Vicsek Model of flocking, particles possesses an internal degree of freedom, such as their director, which is subject to interaction with other particles, provided they are within a certain range. In an effort to understand better the interplay between spatial and internal degrees of freedom, we study numerically a variation of the $q=2$ Potts Model on and off the lattice, where particles are additionally subject to Brownian motion. The lack of a feedback of the internal degrees of freedom to the spatial degrees of freedom renders this model generically non-equilibrium. We confirm previous work that showed that the static exponents of the phase transition are unaffected by the diffusion. In contrast to previous work, we show that the formation of ordered clusters is not undermined by diffusion, but should rather be thought of as an effective form of interaction. We demonstrate how our numerical findings can be understood on the basis of the well-established Model A, B and C: Off lattice, the Brownian $q=2$ Potts Model is Model C. On the lattice, it is Model A with an additional (irrelevant, conserved) Model B noise.