2020/04/18 by Abouzeid M. Shalaby · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevd.101.105006
published as Phys. Rev. D 101, 105006 (2020)
arxiv created 2020/04/18 · arxiv updated 2020/05/13
In this work, we show that one can select different types of Hypergeometric approximants for the resummation of divergent series with different large-order growth factors. Being of n! growth factor, the divergent series for the ε-expansion of the critical exponents of the O(N)-symmetric model is approximated by the Hypergeometric functions k+1Fk-1. The divergent k+1Fk-1 functions are then resummed using their equivalent Meijer-G function representation. The convergence of the resummation results for the exponents ν, η and ω has been shown to improve systematically in going from low order to the highest known six-loops order. Our six-loops resummation results are very competitive to the recent six-loops Borel with conformal mapping predictions and to recent Monte Carlo simulation results. To show that precise results extend for high N values, we listed the five-loops results for ν which are very accurate as well. The recent seven-loops order (g-series) for the renormalization group functions β,γϕ2 and γm2 have been resummed too. Accurate predictions for the critical coupling and the exponents ν, η and ω have been extracted from β,γϕ2 and γm2 approximants.