2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51385Large 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)High Energy Physics - Theorytext