Critical behavior of the 2d scalar theory: resumming the ${\rm N}^8{\rm LO}$ perturbative mass gap

Abstract: We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional $\phi^4$ theory in the $\mathbb{Z}_2$ symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-$g^7$ we obtain $g_c = 2.779(25)$ which compares very well with the state of the art ${\rm N}^8{\rm LO}$ result, $g_c = 2.807(34)$. As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.