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In this work, we use a specific parameterization of the hypergeometricapproximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) toapproximate the seven-loop critical exponent $\nu$ for the $O(2)$-symmetric$\phi^4$ model. Our prediction gives the result $\nu=0.6711(7)$ which iscompatible with the value $\nu=0.6709(1)$ from the famous experiment carried onthe space shuttle Columbia. On the other hand, our result is also compatiblewith recent precise theoretical predictions that are excluding the experimentalresult. These theoretical results include non-perturbative renormalizationgroup calculations ( $\nu=0.6716(6)$), the most precise result from Monte Carlosimulations ($\nu=0.67169(7)$) as well as the recent conformal bootstrapcalculations ($\nu=0.67175(10)$). Although our result is compatible withexperiment, the plot of renormalization group result versus the number of loopssuggests that higher orders are expected to add significantly to accuracy andprecision of the $\nu$ exponent in a way that may favor the theoreticalpredictions.

The $\lambda$-point anomaly in view of the seven-loop Hypergeometric resummation for the critical exponent $\nu$ of the $O(2)$ $\phi^4$ model