Superfast convergence effect in large orders of the perturbative and $ε$ expansions for the O(N) symmetric $ϕ^4$ model

P. V. Pobylitsa

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arXiv · 0807.5136

Superfast convergence effect in large orders of the perturbative and $ε$ expansions for the O(N) symmetric $ϕ^4$ model

P. V. Pobylitsa

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Abstract

Usually the asymptotic behavior for large orders of the perturbation theory is reached rather slowly. However, in the case of the N-component $ϕ^4$ model in D=4 dimensions one can find a special quantity that exhibits an extremely fast convergence to the asymptotic form. A comparison of the available 5-loop result for this quantity with the asymptotic value shows agreement at the 0.1% level. An analogous superfast convergence to the asymptotic form happens in the case of the O(N)-symmetric anharmonic oscillator where this convergence has inverse factorial type. The large orders of the $ε$ expansion for critical exponents manifest a similar effect.

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BibTeX RIS

P. V. Pobylitsa. 2008-08-27. Superfast convergence effect in large orders of the perturbative and $ε$ expansions for the O(N) symmetric $ϕ^4$ model. https://arxiv.org/abs/0807.5136

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