Hypergeometric Gevrey-0 approximation for the Gevrey-k divergent series with application to eight-loop renormalization group functions of the O(N)-symmetric field model - Abouzeid M. Shalaby (16810695) (2024)
Mera et al. (Phys Rev Lett 115:143001, 2015) discovered that the hypergeometric function can serve as an accurate approximant for a divergent Gevrey-1 type of series with an asymptotic large-order behavior of the form . What is strange about this approximant is that it has a series expansion with the wrong large-order behavior (Gevrey-0 type). In this work, we extend this discovery to Gevrey-k series where we show that the hypergeometric approximants and its extension to the generalized hypergeometric approximants are not only able to approximate divergent (Gevrey-1) series but also able to approximate strongly-divergent series of Gevrey-k type with . Moreover, we show that these hypergeometric approximants are able to predict accurate results for the non-perturbative strong-coupling and large-order parameters from weak-coupling data as input. Examples studied here are the ground-state energy for the anharmonic oscillators. The hypergeometric approximants are also used to approximate the recent eight-loop series (g-expansion) of the renormalization group functions for the O(N)-symmetric scalar field model. Form these functions for , and 3, critical exponents are extracted which are very competitive to results from more sophisticated approximation techniques. Other Information Published in: The European Physical Journal Plus License: https://creativecommons.org/licenses/by/4.0 See article on publisher's website: https://dx.doi.org/10.1140/epjp/s13360-024-05373-y