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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 accepted: | May 28, 2024 |
| Date submitted: | May 2, 2024, 12:49 p.m. |
| Submitted by: | Veniamin Abalmasov |
| 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
- 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.
- Following referee 2’s comments, I have moved the discussion of some details into Appendices.
- 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.
Published as SciPost Phys. 16, 151 (2024)
Reports on this Submission
Report #3 by Pranay Patil (Referee 1) on 2024-5-17 (Invited Report)
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Report #2 by Hiroshi Watanabe (Referee 3) on 2024-5-14 (Invited Report)
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Report #1 by Li-Ping Yang (Referee 2) on 2024-5-11 (Invited Report)
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