Critical behavior of the 2d scalar theory: resumming the N8LO perturbative mass gap

Abstract

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ 4 theory in the ℤ2 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 N8LO 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.

Keywords

• Discrete Symmetries
• Nonperturbative Effects