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Spontaneous breaking of finite group symmetries at all temperatures

by Pedro Liendo, Junchen Rong, Haoyu Zhang

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Submission summary

Authors (as registered SciPost users): Junchen Rong
Submission information
Preprint Link:  (pdf)
Date submitted: 2023-01-09 17:05
Submitted by: Rong, Junchen
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases that persist at all temperatures. We work with two $\lambda \phi^4$ theories coupled through their mass terms. The two $\lambda \phi^4$ theories are chosen to preserve either the cubic symmetry group or the tetrahedral symmetry group. A one-loop calculation in the $4-\epsilon$ expansion shows that there exist infinitely many fixed points that can host an all temperature SSB phase. An analysis of the renormalization group (RG) stability matrix of these fixed points, reveals that their spectrum contains at least three relevant operators. In other words, these fixed points are tetracritical points.

Author comments upon resubmission

This is the modified version. The requested changes from the referees have been taken care of.

List of changes

1, As requested by referee 1, we added to sections 2.2 and section 2.3 the discussion of the isotropy of the Tetrahedral(3) and Cubic(3) groups. We also added in section 2.2 the comment that the persistent symmetry-breaking models we found involve at least one cubic group.
1, We mentioned explicitly which of the two groups is broken at finite temperature, as suggested by the referee.2
2, Near the CFT point, our model does have a disordered phase at a lower temperature, while the ordered phase is at a higher temperature. We have further clarified this at the end of the first paragraph.
3, The problem of the missing factor of 3 in the Lagrangian of the cubic(N) theory has been fixed (we have deleted the Lagrangian in section 2.1 since it is not really necessary to mention it there)
4, The symmetry group for the fixed points that are given in table 1 should be Cubic(60)× Cubic(4), we thank the referee for pointing this out.
5,6,7 The typos of indices in eqn (2.7), (2.8), (2.10) and (2.11) have been fixed.
8, We have fixed the mistake in referring to Fig. 1 in Section 2.3

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2023-2-4 (Invited Report)


The authors have adequately addressed the issues mentioned in my previous report and I recommend the paper for publication.

I would like to just point out a minor typo. In the last paragraph of section 2.1 (page 5) where the authors refer to table 1, the case that is mentioned should be Cubic(60)$\times$Cubic(4) instead of Cubic(60)$\times$Cubic(3).

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Anonymous Report 1 on 2023-1-10 (Invited Report)


With the additions and corrections by the authors, I think the manuscript can now be published.

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