Correlation Functions of the Anharmonic Oscillator: Numerical Verification of Two-Loop Corrections to the Large-Order Behavior

TL;DR

This paper numerically verifies two-loop corrections to the large-order behavior of correlation functions in the $O(N)$-anharmonic oscillator, confirming improved agreement with asymptotic estimates when including these corrections.

Contribution

It provides numerical validation of two-loop corrections to large-order behavior in the $O(N)$-anharmonic oscillator, extending previous analytic results.

Findings

Two-loop corrections significantly improve the match between asymptotic estimates and perturbation theory.

Numerical results for $O(1)$, $O(2)$, and $O(3)$ oscillators confirm the analytic predictions.

Enhanced agreement demonstrates the importance of higher-order corrections in large-order analysis.

Abstract

Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us in [L. T. Giorgini et el., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, and 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 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.