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Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class
by Marten Reehorst, Slava Rychkov, Benoit Sirois, Balt C. van Rees
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Submission summary
| Authors (as registered SciPost users): | Marten Reehorst · Slava Rychkov |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.19411v2 (pdf) |
| Date submitted: | July 4, 2024, 2:28 p.m. |
| Submitted by: | Reehorst, Marten |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 \leq d < 4$. Our results show that $N_c> 3.78$ for $d = 3$. This favors the scenario that the physically relevant models with $N = 2,3$ in $d=3$ do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
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Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-9-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2405.19411v2, delivered 2024-09-23, doi: 10.21468/SciPost.Report.9796
Report
The authors study phase transitions in the frustrated magnets, which are described by a matrix model with symmetry O(N)XO(2). They use the conformal bootstrap method and find that no unitary theory can be found in $d=3$ for N smaller than some value that they evaluate at 3.78.
The results obtained in this article are interesting and deserve publication in scipost. There is however few points I would like to raise.
1) In sect. 3.3.2 the authors study the fate of the fixed points C+ and C-, which they relate to minima of their navigator function, as N is decreased. They find that C+ "turns into a saddle". As far as I understand, the navigator function is continuous and there is a finite island where it is negative. Consequently, if C+ becomes a saddle point, local minima must appear at the same time (in agreement with Morse theory). What happens to these minima?
2) If the minimum C+ disapears around N=7, I would expect that, for $3.76<N<7, the island found by the authors corresponds to an unstable fixed point in the renormalization-group sense. The phase transition would be generically of first order except at some tricritical point and Nc(3) would be close to 7, not 3.76. Unfortunately, the authors are unable to compute the scaling dimension of the operator SS' and cannot really test this. An alternative would be that it is not always true that a local minimum can be associated with a fixed point. I would encourage the authors to comment on this.
3) In Fig 8, the curves representing the scaling dimensions of various operators clearly show a feature around 4.2 (a breaking of the slope or maybe a square root). What is at the origin of this behavior?
4) Finally, I think that the references 45 and 46 should appear earlier in the introduction.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #1 by Anonymous (Referee 1) on 2024-7-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2405.19411v2, delivered 2024-07-28, doi: 10.21468/SciPost.Report.9484
Report
The paper is excellently written and all calculations seem correct, so I suggest no changes. Looking ahead, it would be nice to also bootstrap the model with two relevant singlets (this paper only focussed on the model with one relevant singlet), so that they can explicitly see the merger and annihilation of the two fixed points.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)