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

Titelangaben

Völkel, Simeon ; Hartung, Stefan ; Rehberg, Ingo:
Comment on "Hysteretic transition between states of a filled hexagonal magnetic dipole cluster".
Ithaca, NY : Cornell University , 2022
DOI: https://doi.org/10.48550/arXiv.2203.13670

Volltext

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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.