New universality class in three dimensions: The critical Blume-Capel model

Abstract

We study the Blume-Capel universality class in $d=\frac{10}{3}-\epsilon$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\mathrm{MS}}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $\epsilon =\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the OPE coefficients to the leading order. Our findings agree with and complement CFT results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.

arXiv comment5 pages, 1 figure, v2: new title, extended introduction, to appear in PRD

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• Uncovering novel phase structures in ${\square }^k$ scalar theories with the renormalization group
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• Multi-critical ${\square }^k$ scalar theories: A perturbative RG approach with $\epsilon$-expansion
• Platonic Field Theories
• Multi-critical multi-field models: a CFT approach to the leading order
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• The tricritical Ising CFT and conformal bootstrap
• Conformal Data of Fundamental Gauge-Yukawa Theories
• Renormalization of multicritical scalar models in curved space
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• New renormalization group study of the 3-state Potts model and related statistical models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Renormalization of supersymmetric chiral theories in rational spacetime dimensions
• Critical and multicritical Lee-Yang fixed points in the local potential approximation