标题： 蚱蜢模型中对称性破缺的起源 显示英文标题

标题： Origin of Symmetry Breaking in the Grasshopper Model

摘要： 平面跳蚤问题，最初在（Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494）中引入，是具有长程各向同性相互作用的模型的一个显著例子，其基态破坏了旋转对称性。在本工作中，我们分析并解释这种对称性破缺的性质，并强调维度的重要性。有趣的是，在三维情况下，对于小跳跃，旋转对称性得以恢复，这对应于二维问题的非各向同性齿轮轮齿区域。我们讨论了在N维中再现原系统对称性质的简化模型。对于二维空间中的完整跳蚤模型，我们得到了圆盘最优扰动的定量预测。我们的分析结果通过数值模拟得到证实。 显示英文摘要

摘要： The planar grasshopper problem, originally introduced in (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494), is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this work we analyze and explain the nature of this symmetry breaking with emphasis on the importance of dimensionality. Interestingly, rotational symmetry is recovered in three dimensions for small jumps, which correspond to the non-isotropic cogwheel regime of the two-dimensional problem. We discuss simplified models that reproduce the symmetry properties of the original system in N dimensions. For the full grasshopper model in two dimensions we obtain quantitative predictions for optimal perturbations of the disk. Our analytical results are confirmed by numerical simulations.