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Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model
by V. A. Abalmasov
Submission summary
| Authors (as registered SciPost users): | Veniamin Abalmasov |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2310.20385v2 (pdf) |
| Date submitted: | 2024-05-02 12:49 |
| Submitted by: | Abalmasov, Veniamin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Free energy as a function of polarization is calculated for the square-lattice $J_1$-$J_2$ Ising model for $J_2 < |J_1|/2$ using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at $J_2 > |J_1|/4$. These findings enrich our knowledge of the $J_1$-$J_2$ Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
I am grateful to the referees for their interest in the paper, reviews and useful feedback, which helped me make the article clearer and more readable. I have made substantial revisions to the manuscript and hope that the referees and editors will be satisfied with the changes made in response to their comments.
I list the major changes and address the referee’s comments below.
Yours sincerely,
Veniamin Abalmasov
List of changes
List of major changes
1. Following referee 1’s comments, I have considered the dependence of the restricted free energy on nearest-neighbor correlations and added relevant discussions at the end of Sec. 4 and in Appendix B.3. I have also discussed of the RLFA procedure and its ability to encode spatial patterns in Appendix A.2.
2. Following referee 2’s comments, I have moved the discussion of some details into Appendices.
3. Following referee 3’s comments, I have added in Appendix A.2 a discussion of the ability of RLFA to predict the geometric phase transition as opposed to MFA.
Current status:
Reports on this Submission
Report 3 by Pranay Patil on 2024-5-17 (Invited Report)
Report
Author has taken previous suggestions into account and made suitable changes.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report 2 by Hiroshi Watanabe on 2024-5-14 (Invited Report)
Strengths
Calculations and analysis were carefully performed.
Weaknesses
The topic of the paper is somewhat specialized and may not appeal to a broader audience.
Report
The author has appropriately revised the manuscript and has adequately answered all my criticisms. Therefore, I agree with the publication of the manuscript.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report 1 by Li-Ping Yang on 2024-5-11 (Invited Report)
Strengths
careful calculations and comparison
Weaknesses
The size is not enough, but the argument is sufficient.
Report
The author made substantial progress in the calculations and expressions. The discussion of (M,c1,c2) improved the clarity. I recommend to publish.
Recommendation
Publish (meets expectations and criteria for this Journal)