Calculation of Thermodynamic Quantities of 1D Ising Model with Mixed Spin-(s,(2t − 1)/2) by Means of Transfer Matrix

Round 1

Reviewer 1 Report

 The study focuses on a 1D mixed-spin model using a transfer matrix approach. My primary critique is that the model does not truly involve a system of mixed spins. Drawing inspiration from the concept of spin in quantum mechanics, a spin S is defined in classical statistical physics as an integer or half-integer ranging from -S to S. Specifically, a spin 1/2 corresponds to an Ising spin of either +1/2 or -1/2. A spin of 1 can take three values: -1, 0, and 1. This precise definition is used in Ref. [6] for instance. In contrast, the authors exclusively consider Ising spins, albeit with varying magnitudes: half of the spins equal to +s or -s, and the second half to -(2t-1)/2 or +(2t-1)/2. Notably, the model explored by the authors does not involve spins 1. Therefore, any references to mixed spins (or spin-1) should be removed from the paper.

As can be seen in equations (8) and (9), the model is actually an Ising chain with a uniform exchange coupling J and an oscillating magnetic field h,h~,h,h~,h,h~,...

As stated by the authors, the overall physics of this model is globally the same as the Ising chain subjected to a uniform magnetic field. However, a more comprehensive exploration of the differences would have been beneficial. In Figure 4, the magnetization plot exhibits three distinct steps at low temperatures (instead of the usual single one in the Ising chain). This phenomenon can be attributed to either all spins assuming the same state or spins adopting different states within even and odd sublattices. These three distinctive steps subsequently give rise to three peaks in the magnetic susceptibility upon differentiation with respect to h.

Author Response

Dear Referee,

First of all, thank you for your constructive and improving suggestions and comments. You can find attached the report I prepared for your suggestions and comments. I am also revising my article completely and uploading it to the system again. I hope my corrections and additions will be enough for you.

Best regards
Professor Hasan AKIN

Author Response File: Author Response.pdf

Reviewer 2 Report

- Line 3, what is "Under a null boundary condition"? It should be discussed.

- Line 15, the text "In Ref. [6], on the Cayley tree we classified the disordered" is confusing. The author has given the reference of other and at the same time, the authors claim that we classified.

- Line 30, the text "I am not aware of any" should be replaced with "The author is not aware of any".

- Line 31, the text "In this brief essay" should be replaced with "In this paper".

- Line 31, the text "we will use" should be replaced with "we use".

- Line 33, the text "Due to its widespread general application across numerous physical models" should be replaced with "Due to the widespread applications"

- The author looks confusing about writing the paper. Sometimes, the author mentioned "In this brief essay" and sometimes the author mentioned "In this short study". The author should be focus on the write-up of the paper.

- Line 47, the text "We estimate" should be replaced with "We also estimate"

- Throughout the paper, the author says that "We will". The author should the present tense while revising the language of the paper.

- More explanation should be provided for Figure 2.

- More explanation should be provided for Figure 4 that does Figure 4 reveals.

- Line 69, the author says that "It is well-known that the total partition function". Please provide a reference for it.

- The software, package and library used for the visual illustrations should be discussed.

- Throughout the paper, the author says that "We will". The writer of the paper is a single author. Therefore, using "we" does not make sense. Please revise the paper thoroughly. Particularly, the author should write the paper as a third party.

Extensive editing of English language required

Author Response

Dear Referee,

First of all, thank you for your constructive and improving suggestions and comments. You can find attached the report I prepared for your suggestions and comments. I am also revising my article completely and uploading it to the system again. I hope my corrections and additions will be enough for you.

Best regards
Professor Hasan AKIN

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I am satisfied with the modifications made by the authors.

Author Response

Dear Referee 1,

Thank you very much for the referee's valuable suggestions and comments. In line with these suggestions, I revised my article for the second time. I have made numerous corrections, especially by thoroughly checking grammar and misspellings. I marked the corrections in blue. I hope this final revised version is ready for publication.
Kind regards
Hasan

Reviewer 2 Report

The authors have incorporated my comments. 

Minor editing of English language required

Author Response

Dear Referee 2,

Thank you very much for the your valuable suggestions and comments. In line with your suggestions, I revised my article for the second time. I have made numerous corrections, especially by thoroughly checking grammar and misspellings. I marked the corrections in blue. I hope this final revised version is ready for publication.
Kind regards
Hasan