Local variations of the magnetization effected by an external field in molecular rings

The manuscript presents a classical numerical study of magnetization behavior in rings of antiferromagnetically coupled icosahedra. The author investigates how external magnetic fields induce magnetization discontinuities and symmetry-breaking effects depending on the ring size and parity. The topic is relevant to the field of frustrated spin systems, and the results are carefully obtained.
While the study is technically sound, the manuscript in its current form has several limitations that, in my view, should be addressed. These are summarized below.

Main comments:
1)Model clarity
a) The connection scheme between icosahedra is not fully described. In particular, it is unclear how the icosahedra are joined into triangles or hexagons — which specific vertices are involved in the inter-icosahedral coupling? This could be clarified with a schematic illustration.
b) Figure 1 is schematic and not a true planar projection; it does not reflect the full icosahedral geometry. I would suggest replacing "planar projection" with a phrase such as "2D schematic representation of interacting icosahedra" to avoid confusion.
2)Lack of explanation for modeling choices
c) The selection of the parameter \omega = \pi/10ω=π/10 is not justified.
d) The polar angle \theta_i is not mathematically defined. How exactly is it calculated?
3)Presentation and style
e) The manuscript is dense and would benefit from more explanatory context, especially concerning modeling assumptions and the interpretation of results.
4)Figures
f) Graphs would benefit from clearer labeling or color-coding to distinguish individual icosahedra or data series.
g) Figure 16 could be incorporated as an inset into Figure 15 instead of appearing as a separate figure.

Recommendation:
The author has indicated that the manuscript opens a new pathway in an existing or new research direction. While the work is technically sound, I do not find that this claim is convincingly supported. The manuscript does not clearly articulate a broader conceptual shift or a compelling outlook for multi-pronged follow-up research.
I therefore recommend that the submission be considered for SciPost Physics Core, where it would be better aligned with the expected scope and contribution level.

Accept in alternative Journal (see Report)

This is a manuscript on classical spin systems employing the Heisenberg model.
The author investigates interacting icosahedra. Icosahedra with nearest neighbor antiferromagnetic interactions show interesting frustration effects.
Here the author combines up to 6 of them into a one-dimensional arrangement.
He discovers an interesting and unexpected magnetization behavior.

The paper studies a novel spin system in a classical approximation. The manuscript needs major revision in view of the above comments.

See 1-7 in weaknesses.

Ask for major revision

Review of
N. P. Konstantinidis:
Local variations of the magnetization effected by an external field in molecular rings

The present work deals with the magnetization at zero temperature for certain classical spin systems. These are formed from rings of icosahedra coupled with double bonds. This is an interesting topic and the author presents extensive calculations that make a solid impression. However, I have a fundamental objection which, in my opinion, necessitates a revision of the layout of the work. I will therefore postpone a detailed discussion of the work until a later date, when this revision is available (or my objection has been refuted).

The ground state of an antiferromagnetic icosahedron without a magnetic field is already frustrated and has an energy of -\sqrt{5}/5 per bond, which is above the theoretical minimum of -1. By coupling several icosahedra, taking into account the cyclic boundary condition, the ground state energy could rise further above the possible minimum value. If this does not happen, we call the ground state “minimally frustrated”. In this case, the energy of the bonds in the icosahedra is still -\sqrt{5}/5, while the value -1 is added for each bond between the icosahedra (for simplicity, I assume that all bonds have the value +1). The author now claims that for minimally frustrated systems, the number of icosahedra must be a multiple of 3, but without convincingly justifying this. I think, however, that rings with an even number of icosahedra are always minimally frustrated, whereas rings with an odd number are not. In the case N=3, this would collide with the author's statements. In this case the minimum energy is approx. 2% above the minimally frustrated minimum, which can easily be verified numerically. If this is true, then an investigation of only cases N=3 and N=6 might be unfounded; one would rather think of cases N=3,4,5,6. However, these are questions that only arise once the problem addressed has been clarified.

Ask for major revision