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

TL;DR

This paper clarifies the nature of two instabilities in a hysteretic transition of a magnetic dipole cluster, identifying them as a symmetry-breaking bifurcation and a fold with specific scaling behaviors.

Contribution

It provides a detailed analysis of the instabilities, revealing their true nature as a symmetry-breaking bifurcation and a fold, which was previously left unanswered.

Findings

First instability is a symmetry-breaking sub-critical bifurcation.

Second instability is a fold with semi-cubic parabola scaling.

Clarifies the transition mechanisms in magnetic dipole clusters.

Abstract

In the paper "Andrew D.P. Smith, Peter T. Haugen, Boyd F. Edwards: Hysteretic transition between states of a filled hexagonal magnetic dipole cluster, Journal of Magnetism and Magnetic Materials 549 (2022): 168991" 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.