Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model

Round 1

Reviewer 1 Report

Manuscript number: entropy-1295917 Entropy MDPI (type: article)

TITLE: Short-range Berezinskii-Kosterlitz-Thouless phase characterization for the q-state clock model

AUTHORS: Oscar A. Negrete, Patricio Vargas, Francisco J. Peña, Gonzalo Saravia, and Eugenio E. Vogel

The first review of the manuscript

Overall description of the manuscript

In the manuscript entitled “Short-range Berezinskii-Kosterlitz-Thouless phase characterization for the q-state clock model” by Oscar A. Negrete, Patricio Vargas, Francisco J. Peña, Gonzalo Saravia, and Eugenio E. Vogel, the authors investigate the q-state clock model by means of the classical Monte Carlo methods focusing on analysis of newly introduced order-parameters. This allows to understand the mechanisms of two different transitions which occurs in the system analyzed for q>4. The paper stars with very nice introduction and model description section, which contain all necessary information, provide all required literature context and clearly states the problem investigated. Next, the methodology is clearly described, what allows to check and reobtain the results for other groups. The numerical results are clearly presented and the conclusions are supported by the findings.

The paper fits very well the journal scope. The English language in the manuscript is relatively good. The paper is well written and, together with the results it includes, it could fulfill requirements to be a good scientific article. In my opinion, the manuscript can be understood even by the non-specialist in the field, what is not very common nowadays and it should be considered a huge advantage. The paper has 13 pages and includes, 36 references (2 pages) – I did not notice any excessive self-citations, and 11 figures (equivalent 3.5 pages) – effectively about 8 pages of the main text. The authors refer to the most recent and most appropriate work. All diagrams (figures) are very clear and essential and their captions are informative. The title clearly and concisely conveys the topic of the article.

In my opinion the manuscript might be published after minor revisions. I believe that suggested improvements can increase the readability of the paper. My comments are only associated to presentation of the results and, but it is also a very important issue.

Some specific comments of minor importance that should be addressed by the authors (I have only one comment):

1) lines 39-41, page 2: this part of text does not provide any information for the paper. The authors do not consider any anisotropy or external magnetic field further in the text so the equation (2) is redundant. Even, any references are cited in this context. This part of text should be removed in my opinion.

2) line 48, page 2: the abbreviation “FP” is not defined. It is probably for “Ferromagnetic  phase” but it should be clearly states, as every acronym should be defined, where it appears.Definition of FP appears in line 51. Please correct.

3) the authors should decide if the use “the BKT phase” or “the VP”, e.g. line 62, page 2. Using both two term can be misleading and introduces confusion. Please go through the whole text of the manuscript.

4) line 80, page 2: the word “condensates” does not fit in the context. It would be better to use “includes”.

5) page 3, equation between lines 90-91: as I correctly understood Si are vectors (in line 91 it indeed has two components), thus m is also vector. So arrows above symbols are necessary (such notation is used in equation (1). In such case, definition (3) is not confusing. Please correct.

6) line 134, page 4: maybe some reference /link could be provided for wlzip, where it is described in more details?

7) line 162, page 5: probably “next” should be change into “above”. In lines 150-161 the procesure is described for q=8, whereas in lines 162-169 is generalized. Please check.

8) I do not see second maximum for q>4 in Figures 5 and 6 corresponding to transition between FF and FV phases. Maybe it is quite weak. Please comment.

9) line 208, page 8: change “Eq. 10” into “Eq. (10)” – missing brackets.

10) line 233, page 9: the authors write: “…two-spin parameters with two main differences: The amplitude of the curve is lower since they are less abundant, and the curve maximizes near 1.0 since spins need to be freer to articulate a series of two consecutive …”. Amplitude of which curve is discussed? I see that amplitude of diversity of C3 is larger. This sentence is not clear for me and should be reformulated.

11) lines 270-272, page 10: the authors write: “In the case of the highest transition temperature it is the temperature derivative of C03 the one that is better defined in consonance with the better defined inset of Fig 8 as compared to the inset of Fig. 9.” I have problems with understanding this sentence. It is not clear. Please clarify and reformulate this text.

To sum up, after these issues will be resolved, I strongly believe this paper could become suitable for publication in “Entropy” MDPI journal as an article provided that the authors introduce required changes. The topic of the paper, which is strongly associated to fundamental physics of two dimensional spin system. Thus, I think that any work investigating and discussing these issues is highly demanded by the scientific community.

Author Response

Dear referee, please review the attached pdf. 

Much appreciated,

Patricio Vargas on behalf of all the authors.

Author Response File: Author Response.pdf

Reviewer 2 Report

The Authors using information theory definitions perform an analysis of the classical order parameters of Berezinskii-Kosterlitz-Thouless phase, within a suitable XY model. They show that using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions exhibited by this system for large q. Interestingly, the appearance at relatively low temperatures and disappearance of the BKT phase at higher temperatures is univocally determined by the short-range interactions recognized by the information content of classical and specific parameters.

In my opinion the paper could be published if the Author properly addresses the following minor points:

• I suggest to the Authors to correctly quote Eqs.(1)-(2) as Hamiltonians rather than energy.
• Since Fig. 4 shows that information theory parameters as function of temperature exhibit similar behavior, i.e. the location of the maximum as well as the knee at low temperatures, I suggest to comment on the physical contents of these parameters as well as their relationship. I think, indeed, that the physical information related to any parameter is the same, so that they are probably analytically related.  

Author Response

Dear referee, please review the attached pdf. 

Much appreciated,

Patricio Vargas on behalf of all the authors.

Author Response File: Author Response.pdf