Operator product expansion coefficients from the nonperturbative functional renormalization group

Abstract

Using the nonperturbative functional renormalization group (FRG) within the Blaizot-Méndez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient $c_{112}$ associated with the operators ${\mathcal{O}}_1\sim \phi$ and ${\mathcal{O}}_2\sim {\phi }^2$ in the three-dimensional $\mathrm{O}(N)$ universality class and in the Ising universality class ($N=1$) in dimensions $2\le d\le 4$. When available, exact results and estimates from the conformal bootstrap and Monte-Carlo simulations compare extremely well to our results, while FRG is able to provide values across the whole range of $d$ and $N$ considered.

arXiv comment11 pages, 4 figures. Final version

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