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Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models

Pelissetto, A. and Vicari, E. (1998) Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models. Nuclear Physics B, 519 . p. 626. ISSN 1873-1562

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We investigate some issues concerning the zero-momentum four-point renormalized coupling constant g in the symmetric phase of O(N) models, and the corresponding Callan-Symanzik beta-function. In the framework of the 1/N expansion we show that the Callan- Symanzik beta-function is non-analytic at its zero, i.e. at the fixed-point value g^* of g. This fact calls for a check of the actual accuracy of the determination of g^* from the resummation of the d=3 perturbative g-expansion, which is usually performed assuming analyticity of the beta-function. Two alternative approaches are exploited. We extend the \epsilon-expansion of g^* to O(\epsilon^4). Quite accurate estimates of g^* are then obtained by an analysis exploiting the analytic behavior of g^* as function of d and the known values of g^* for lower-dimensional O(N) models, i.e. for d=2,1,0. Accurate estimates of g^* are also obtained by a reanalysis of the strong-coupling expansion of lattice N-vector models allowing for the leading confluent singularity. The agreement among the g-, \epsilon-, and strong-coupling expansion results is good for all N. However, at N=0,1, \epsilon- and strong-coupling expansion favor values of g^* which are sligthly lower than those obtained by the resummation of the g-expansion assuming analyticity in the Callan-Symanzik beta-function.

Item Type: Article
Additional Information: Imported from arXiv
Subjects: Area02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici
Divisions: Dipartimenti (from 2013) > DIPARTIMENTO DI FISICA
Depositing User: dott.ssa Sandra Faita
Date Deposited: 14 Feb 2014 12:28
Last Modified: 14 Feb 2014 12:28
URI: http://eprints.adm.unipi.it/id/eprint/1737

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