Spontaneous breaking of finite group symmetries at all temperatures

TL;DR

This paper investigates conformal field theories with finite group symmetries, demonstrating the existence of fixed points that support spontaneous symmetry breaking at all temperatures through a one-loop RG analysis.

Contribution

It introduces a novel analysis of coupled $bbb4$ theories with finite group symmetries, revealing infinitely many fixed points with persistent SSB phases at all temperatures.

Findings

Existence of infinitely many fixed points with all-temperature SSB phases.

Fixed points are tetracritical with at least three relevant operators.

RG analysis shows stability and symmetry-breaking properties of these fixed points.

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 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.