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.
Correlation functions of the anharmonic oscillator: numerical verification of two-loop corrections to the large-order behavior
Malatesta, Enrico M.;
2022
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.
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