Precise critical exponents of the O (N) -symmetric quantum field model using hypergeometric-Meijer resummation

Abstract

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 µ expansion of the critical exponents of the O(N)-symmetric model is approximated by the hypergeometric functions Fk+1k-1. The divergent Fk+1k-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-loop order. Our six-loop resummation results are very competitive to the recent six-loop 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-loop results for ν which are very accurate as well. The recent seven-loop order (g series) for the renormalization group functions β,γφ2, and γm2 has 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.