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

TL;DR

This paper uses optimized perturbation theory to resum high-order series for the mass gap in 2D scalar $^4$ theory, achieving results close to state-of-the-art calculations and exploring the supercritical region for additional insights.

Contribution

It applies OPT to high-order resummation of the mass gap series in 2D scalar theory, including supercritical region analysis, providing results consistent with advanced perturbative calculations.

Findings

At order-$g^7$, the critical coupling $g_c$ is 2.779(25).

OPT yields results close to ${ m N}^8{ m LO}$ calculations.

Supercritical region analysis offers useful extrapolation insights.

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.