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. This provides a counterexample to the well-known argument that the mobility of particles is the key origin of the spontaneous symmetry breaking in two-dimensional Vicsek type models. Our result suggests that the origin of the symmetry breaking should be sought in the absence of a detailed balance condition, or, equivalently, in nonequilibrium nature.

中文翻译：

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植绒平衡模型的Hohenberg-Mermin-Wagner型定理

我们研究了一类具有Vicsek类型“交换相互作用”的经典硬核颗粒的二维模型，该模型使附近颗粒的运动方向对齐。通过扩展没有自发磁化的Hohenberg-Mermin-Wagner定理和相关函数的McBryan-Spencer界，我们证明了模型在任何非零温度下都不会在平衡状态下自发地破坏旋转对称性。这为众所周知的论点提供了反例，该论点是粒子的迁移率是二维Vicsek类型模型中自发对称性破坏的关键根源。我们的结果表明，应该在没有详细的平衡条件的情况下，或者等效地，在非平衡性质下，寻找对称破坏的起源。