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)PRVDAQ2470-001010.1103/PhysRevD.101.125001]. 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.
L. T. Giorgini et al., "Correlation Functions of the Anharmonic Oscillator: Numerical Verification of Two-Loop Corrections to the Large-Order Behavior," Physical Review D, vol. 105, no. 10, article no. 105012, American Physical Society, May 2022.
The definitive version is available at https://doi.org/10.1103/PhysRevD.105.105012
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15 May 2022