On the Accuracy of Resummation Methods in the O(N) ϕ⁴ Model with Increasing N

Both QED and the O(N)-symmetric ϕ⁴ field theory exhibit divergent but asymptotic perturbative series. While reliable results in the ϕ⁴ model require resummation methods, QED achieves remarkable accuracy from the naive series alone due to the smallness of the fine-structure constant. In our recent work (Eur. Phys. J. C 85, 751 (2025)), we show that as N increases in the O(N) model, a QED-like feature emerges: the effective perturbative parameter decreases, enhancing the accuracy of naive expansions. In this talk, we explore how this behavior influences the accuracy within  the calculation of the critical exponents.