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 c112 associated with the operators O1 ∼ ϕ and O2 ∼ ϕ 2 in the three-dimensional O(N ) universality class and in the Ising universality class (N = 1) in dimensions 2 ≤ d ≤ 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.