Large order asymptotics and convergent perturbation theory for critical indices of the ϕ⁴ model in 4-ε expansion

2002/07/01 by J. Honkonen, M. Komarova, M. Nalimov
Physics and Astronomy · #hep-th

paper · pdf

published as Acta Phys.Slov. 52 (2002) 303-310 · 8 pages, 2 figures. Invited talk at the 5th International Conference Renormalization Group 2002 (High Tatra Mountains, Slovakia, 10-16 March 2002)

arxiv created 2002/07/01 · arxiv updated 2009/11/30

Abstract

Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the ϕ⁴ (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 ϕ⁴ (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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