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arXiv · 1706.06887

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

Alessandro Codello·Mahmoud Safari·Gian Paolo Vacca·Omar Zanusso
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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 $\overline{\rm MS}$. 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.

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Alessandro Codello, Mahmoud Safari, Gian Paolo Vacca, Omar Zanusso. 2017-06-21. New universality class in three dimensions: The critical Blume-Capel model. https://doi.org/10.1103/physrevd.96.081701

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