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

Honkonen, J.; Komarova, M.; Nalimov, M.

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

Authors

Honkonen, J.

Komarova, M.

Nalimov, M.

Description

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.
8 pages, 2 figures. Invited talk at the 5th International Conference Renormalization Group 2002 (High Tatra Mountains, Slovakia, 10-16 March 2002)