SciPost Submission Page
Non-gaussianity of the critical 3d Ising model
by Slava Rychkov, David Simmons-Duffin, Bernardo Zan
Submission summary
| Authors (as registered SciPost users): | Slava Rychkov |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1612.02436v2 (pdf) |
| Date accepted: | Feb. 8, 2017 |
| Date submitted: | Dec. 22, 2016, 1 a.m. |
| Submitted by: | Slava Rychkov |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results. We focus on the non-gaussianity Q - the ratio of the 4pt function to its gaussian part given by three Wick contractions. This ratio reveals significant non-gaussianity of the critical fluctuations. The bootstrap results are consistent with a rigorous inequality due to Lebowitz and Aizenman, which limits Q to lie between 1/3 and 1.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2017-1-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1612.02436v2, delivered 2017-01-30, doi: 10.21468/SciPost.Report.72
Strengths
1- interesting subject 2- high precision numerical analysis 3- interesting relation with lattice results
Weaknesses
1- too concise on some technical aspects
Report
In particular, the author studies the ratio between this four point function and the same quantity if the Wick theorem could be applied in this case. The deviation of this ratio from 1 tells about the non-gaussianity of the model.
The main result is shown in Fig. 1, which is very suggestive, given its qualitative similarity with respect to the result of the same analysis for the 2d critical Ising model. The authors also verify that their result is compatible with certain inequalities found by Lebowitz and Aizenman through a lattice analysis.
The paper is very interesting and well written. The results are presented in a clear way and I am sure that they will lead to further
insights in the analysis of the critical 3d Ising model.
I definitely support the publication of the paper in the present form.
Requested changes
no changes
Report #1 by Anonymous (Referee 1) on 2017-1-22 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1612.02436v2, delivered 2017-01-22, doi: 10.21468/SciPost.Report.68
Strengths
2-The authors provide a very clear and quantitative measure of the non-Gaussianity of the 3D Ising universality class
Weaknesses
Report
I appreciated also the comparison of the conformal bootstrap results to rigorous inequalities obtained from the lattice model, that are nicely re-derived in the Appendix.
Requested changes
No changes are required