Critical exponents from the weak-coupling, strong-coupling and large-order parametrization of the hypergeometric (k+1Fk) approximants

In this work, we suggest a new parametrization for the hypergeometric (F-k+1(k)) approximants introduced by Mera et al. (2015). The new parametrization enables the approximants to accommodate all perturbative and non-perturbative information of the divergent series as input. Also, the parametrization has been shown to account for the n! growth factor of the given perturbation series provided that one of the denominator parameters of the hypergeometric approximant takes large values. The algorithm with the new parametrization has been tested using two quantum mechanical problems where one can incorporate the weak-coupling, strong-coupling and large-order information. Accurate results have been obtained in using a relatively low order from the perturbation series. Since strong-coupling behavior is not yet known for the renormalization group functions of the O(N)-symmetric phi(4) theory, we used weak-coupling and large-order parametrization to resum the seven-loop critical exponents nu, eta and omega for N = 0, 1, 2, 3, 4. In view of the recent results from six-loop resummation as well as Monte Carlo simulations and conformal bootstrap calculations, our results show a clear improvement to the six-loop results. (C) 2021 The Author(s). Published by Elsevier Inc.

Automated summary

We propose a new parametrization for hypergeometric approximants to accommodate perturbative and non-perturbative information, which has shown promising results in quantum mechanical problems. Our approach leads to accurate results with a relatively low order from perturbation series and demonstrates a clear improvement over previous six-loop results.