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.

arXiv commentFor more accuracy some sentences have been rephrased in this v2. 16 pages, 6 figures

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Cited by in corpus (5)

• Hamiltonian Truncation Effective Theory
• The Breakdown of Resummed Perturbation Theory at High Energies
• Restoration of a Spontaneously Broken Symmetry in an Euclidean Quantum $\lambda {\phi }_{d+1}^4$ model with Quenched Disorder
• Tadpoles and vacuum bubbles in light-front quantization
• Quantum phase transitions in a bidimensional $O(N)\times {\mathbb{Z}}_2$ scalar field model