We study the scaling dimension $\Delta_{\phi^n}$ of the operator $\phi^n$ where $\phi$ is the fundamental complex field of the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$. Even for a perturbatively small fixed point coupling $\lambda_*$, standard perturbation theory breaks down for sufficiently large $\lambda_*n$... (read more)

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