Comment on Hysteretic transition between states of a filled hexagonal magnetic dipole cluster

In the paper Smith et al. (2022) a hysteretic transition between two stable arrangements of a cluster of seven dipoles is presented. The relative strength of the center dipole in a hexagonal arrangement serves as the bifurcation parameter. The authors clearly demonstrate the existence of two instabilities accompanied by discontinuous jumps of the dipole arrangement, but leave the question about the nature of these instabilities unanswered. This comment clarifies the nature of the two instabilities: the first one is a symmetry-breaking sub-critical bifurcation with parabolic scaling of the magnetic potential energy difference between the two branches, and the second one is a fold with its characteristic scaling in the form of a semi-cubic parabola.

Automated summary

This paper examines the hysteretic transition between two stable arrangements of a cluster of seven dipoles, and clarifies the nature of the two instabilities. The first one is a symmetry-breaking sub-critical bifurcation, and the second one is a fold.