Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comment on "Hysteretic transition between states of a filled hexagonal
  magnetic dipole cluster"   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.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int