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

We study the Blume-Capel universality class in $d=\frac{10}{3}-ϵ$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\mathrm{M}\mathrm{S}}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $ϵ=\frac{1}{3}<1$. 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.