论文标题
具有离散方向的极性羊群：接近Vicsek模型的活动时钟模型
Polar flocks with discretized directions: the active clock model approaching the Vicsek model
论文作者
论文摘要
我们将二维$ Q $ Q $ - 状态活动时钟模型（ACM）视为描述羊群的Vicsek模型（VM）的自然离散化。 ACM由能够以$ Q $等距方向在平面中移动的粒子组成，如Active Potts模型（APM）中，其对齐相互作用受铁磁平衡时钟模型的启发。我们发现，对于少数方向，ACM的植入过渡具有与APM相同的现象学，包括巨摩相的分离和重新定位转变。对于较大的方向，ACM中的植入过渡变得等同于VM之一，并显示显微合机的分离和仅横向带，即无重新定位跃迁。同时，ACM的$ q \ to \ infty $限制的过渡，即Active XY模型（AXYM）与VM相同的通用类别。我们还为类似于VM的ACM和AXYM构建了粗粒的流体动力描述。
We consider the off-lattice two-dimensional $q$-state active clock model (ACM) as a natural discretization of the Vicsek model (VM) describing flocking. The ACM consists of particles able to move in the plane in a discrete set of $q$ equidistant angular directions, as in the active Potts model (APM), with an alignment interaction inspired by the ferromagnetic equilibrium clock model. We find that for a small number of directions, the flocking transition of the ACM has the same phenomenology as the APM, including macrophase separation and reorientation transition. For a larger number of directions, the flocking transition in the ACM becomes equivalent to the one of the VM and displays microphase separation and only transverse bands, i.e. no re-orientation transition. Concomitantly also the transition of the $q\to\infty$ limit of the ACM, the active XY model (AXYM), is in the same universality class as the VM. We also construct a coarse-grained hydrodynamic description for the ACM and AXYM akin to the VM.
