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

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Ludovico T. Giorgini, Ulrich D. Jentschura, Enrico M. Malatesta, Giorgio Parisi, Tommaso Rizzo, Jean Zinn-Justin

High Energy Physics - Theory · Submitted 24 Nov 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2111.12765 (version 2)
Pith IDAOYE22LR, Pith's permanent record of this paper and its review
CitationEnrico M. Malatesta, Giorgio Parisi, Jean Zinn-Justin, Ludovico T. Giorgini, Tommaso Rizzo, Ulrich D. Jentschura. "Correlation Functions of the Anharmonic Oscillator: Numerical Verification of Two-Loop Corrections to the Large-Order Behavior." arXiv:2111.12765 (2021). https://pith.science/paper/AOYE22LR
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,752 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.24 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.91 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us in [L. T. background 0.97 0.50 0.03 asserted 0.95
s1 Giorgini et el., Phys. Rev. D 101, 125001 (2020)]. background 0.99 0.09 0.03 unclear 0.61
s2 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. background 0.38 0.50 0.09 asserted 1.00
s3 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. contribution 0.95 0.89 0.77 asserted 0.81

What kind of paper the classifier reports this is: simulation study 0.83 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

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