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

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

2008-07-31

arxiv.org/abs/0807.5136v3

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, typos corrected

Scientific paper

Usually the asymptotic behavior for large orders of the perturbation theory is reached rather slowly. However, in the case of the N-component $\phi^4$ 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 $\epsilon$ expansion for critical exponents manifest a similar effect.

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