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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:  https://arxiv.org/abs/2205.13964v4 (pdf) 
Date submitted:  20230109 17:05 
Submitted by:  Rong, Junchen 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
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 oneloop 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
List of changes
REPLY TO REVIEWER 1
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 symmetrybreaking models we found involve at least one cubic group.
REPLY TO REVIEWER 12
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
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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).