Large order asymptotics and convergent perturbation theory for critical indices of the $ϕ^4$ model in ${4-ε}$ expansion

J. Honkonen; M. Komarova; M. Nalimov

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arXiv · hep-th/0207011

Large order asymptotics and convergent perturbation theory for critical indices of the $ϕ^4$ model in ${4-ε}$ expansion

J. Honkonen·M. Komarova·M. Nalimov

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Abstract

Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the $ϕ^4$ $(4-ε)$ theory is discussed. Well-known results of the asymptotic $4-ε$ expansion of critical indices are shown to be far from the large order asymptotic value. A {\em convergent} series for the model $ϕ^4$ $(4-ε)$ is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the $4-ε$ scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed.

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J. Honkonen, M. Komarova, M. Nalimov. 2002-07-01. Large order asymptotics and convergent perturbation theory for critical indices of the $ϕ^4$ model in ${4-ε}$ expansion. https://arxiv.org/abs/hep-th/0207011

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