论文标题
Hohenberg-Mermin-Wagner型定理，用于羊群平衡模型
Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
论文作者
论文摘要
我们研究了具有Vicsek型“交换相互作用”的经典硬核颗粒的一类二维模型，这些模型与附近颗粒的运动方向相吻合。通过扩展没有自发磁化的Hohenberg-Mermin-Wagner定理和用于相关函数的McBryan-Spencer结合，我们证明这些模型不会自发地破坏任何非零温度下其平衡状态中的旋转对称性。因此，我们得出的结论是，仅粒子的迁移率并不能解释Vicsek型模型中自发的对称性破坏。在没有详细的平衡条件的情况下，必须寻求对称性破裂的起源，或者等效于非平衡性质。
We study a class of two-dimensional models of classical hard-core particles with Vicsek-type "exchange interaction" that aligns the directions of motion of nearby particles. By extending the Hohenberg-Mermin-Wagner theorem for the absence of spontaneous magnetization and the McBryan-Spencer bound for correlation functions, we prove that the models do not spontaneously break the rotational symmetry in their equilibrium states at any nonzero temperature. We thus conclude that the mobility of particles alone does not account for the spontaneous symmetry breaking in Vicsek type models. The origin of the symmetry breaking must be sought in the absence of detailed balance condition, or, equivalently, in the nonequilibrium nature.
