Correlation functions of the anharmonic oscillator: Numerical verification of two-loop corrections to the large-order behavior

Abstract

Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us [L. T. Giorgini et al., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the $O(1)$, $O(2)$, and $O(3)$ oscillators, and we demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop corrections to the large-order behavior.