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

A bstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ 4 theory in the 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 N 8 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.