With an ultraviolet cutoff, the renormalized mean-field perturbation series for φ⁴ theory in four dimensions is locally Borel summable and asymptotic to the non-perturbative trivial solution.
Feldman et al.QED: A proof of renormalizability, Lecture notes in Physics
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Triviality vs perturbation theory: an analysis for mean-field $\varphi^4$-theory in four dimensions
With an ultraviolet cutoff, the renormalized mean-field perturbation series for φ⁴ theory in four dimensions is locally Borel summable and asymptotic to the non-perturbative trivial solution.