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

Abstract

We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ${\varphi }^4$ 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 ${\mathrm{N}}^8\mathrm{LO}$ 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.

Comments: For more accuracy some sentences have been rephrased in this v2. 16 pages, 6 figures