29 July 1999 Ž . Physics Letters B 459 1999 582–588 Convergent expansion for critical exponents ž/ 4 in the On -symmetric f model for large e Juha Honkonen a,1 , Mikhail Nalimov b,2 a ( ) Theory DiÕision, Department of Physics, P.O. Box 9 SiltaÕuorenpenger 20 C , FIN-00014 UniÕersity of Helsinki, Finland b Faculty of Physics, St.-Petersburg UniÕersity, 198904, Ul’yanoÕskaya 1, St. Petergof, St.-Petersburg, Russia Received 31 March 1999; received in revised form 7 June 1999 Editor: P.V. Landshoff Abstract Ž. 4 A modification of the usual perturbation expansion of the n-component On -symmetric f model, which leads to Ž . convergent series, is explicitly renormalized with an infinite set of counterterms. Renormalization-group RG equations with only one coupling constant are derived and shown to govern the large-scale asymptotic behavior of the model. A new expansion is constructed for the critical exponents h and n , which leads to numerical values in good agreement with Borel-transform based estimates and lattice results. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 64.60.Fr; 11.10.Hi; 05.70.Jk Ž. 4 Keywords: Renormalization group; On -symmetric f model; Convergent series for critical exponents The renormalization-group approach to the inves- tigation of critical phenomena has been extremely wx successful 1 . However, the values of, e.g. critical exponents calculated in the e s 4 y d expansion for realistic values of e and n are far from the values determined by experiments or lattice calculations. This is due to the asymptotic character of the wx perturbation expansion 2 . Divergences of expansion series are common in quantum-field theories, but usually they are not essential there due to very small Ž expansion parameter e.g. 1r137 in quantum electro- 1 E-mail: address: juha.honkonen@helsinki.fi; Requests of list- ings of full expressions of the RG coefficient functions should be sent to this address. 2 E-mail: nalimov@snoopy.phys.spbu.ru . dynamics . Contrary to this, in the theory of critical behavior resumming of the perturbation series is called for, since the real parameter of expansion is not small. To obtain results in better agreement with experimental data and lattice-model results, Borel- Leroy transform has been successfully used both in w x w x fixed dimension 3,4 and in the e expansion 4–6 . Results in good agreement with these have been also produced by recent calculations with the use of wx simple Pade-Borel method 7 as well as self-similar ´ wx exponential approximants 8 . All these calculations are based on the divergent series of the usual perturbation expansion. We sug- gest a different approach with the use of a modified Ž. 4 wx expansion for the On -symmetrical f model 9, which leads to conÕergent series. The usual action 0370-2693r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. Ž . PII: S0370-2693 99 00704-2