TY - JOUR
T1 - Origin of symmetry breaking in the grasshopper model
AU - Llamas, David
AU - Kent-Dobias, Jaron
AU - Chen, Kun
AU - Kent, Adrian
AU - Goulko, Olga
N1 - Publisher Copyright:
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2024/4
Y1 - 2024/4
N2 - The planar grasshopper problem, originally introduced by Goulko and Kent [Proc. R. Soc. A 473, 20170494 (2017)10.1098/rspa.2017.0494], is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this paper 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 nonisotropic 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.
AB - The planar grasshopper problem, originally introduced by Goulko and Kent [Proc. R. Soc. A 473, 20170494 (2017)10.1098/rspa.2017.0494], is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this paper 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 nonisotropic 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.
UR - https://www.scopus.com/pages/publications/85195285875
UR - https://www.scopus.com/pages/publications/85195285875#tab=citedBy
U2 - 10.1103/PhysRevResearch.6.023235
DO - 10.1103/PhysRevResearch.6.023235
M3 - Article
AN - SCOPUS:85195285875
SN - 2643-1564
VL - 6
JO - Physical Review Research
JF - Physical Review Research
IS - 2
M1 - 023235
ER -