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.

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

References in corpus (1)

• Generalized Wilson-Fisher critical points from the conformal OPE

Cited by in corpus (3)

• Platonic Field Theories
• Multi-critical multi-field models: a CFT approach to the leading order
• Renormalization of supersymmetric chiral theories in rational spacetime dimensions