  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.
