Nonperturbative renormalization group and momentum dependence of n-point functions. II

Jean-Paul Blaizot, Ramón Méndez-Galain, and Nicolás Wschebor
Phys. Rev. E 74, 051117 – Published 21 November 2006

Abstract

In a companion paper [Blaizot et al., Phys. Rev. E 74, 051116 (2006)], we have presented an approximation scheme to solve the nonperturbative renormalization group equations that allows the calculation of the n-point functions for arbitrary values of the external momenta. The method was applied in its leading order to the calculation of the self-energy of the O(N) model in the critical regime. The purpose of the present paper is to extend this study to the next-to-leading order of the approximation scheme. This involves the calculation of the four-point function at leading order, where interesting features arise, related to the occurrence of exceptional configurations of momenta in the flow equations. These require a special treatment, inviting us to improve the straightforward iteration scheme that we originally proposed. The final result for the self-energy at next-to-leading order exhibits a remarkable improvement as compared to the leading order calculation. This is demonstrated by the calculation of the shift ΔTc, caused by weak interactions, in the temperature of Bose-Einstein condensation. This quantity depends on the self-energy at all momentum scales and can be used as a benchmark of the approximation. The improved next-to-leading order calculation of the self-energy presented in this paper leads to excellent agreement with lattice data and is within 4% of the exact large N result.

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  • Received 31 March 2006

DOI:https://doi.org/10.1103/PhysRevE.74.051117

©2006 American Physical Society

Authors & Affiliations

Jean-Paul Blaizot*

  • ECT*, Villa Tambosi, strada delle Tabarelle 286, 38050 Villazzano (TN), Italy

Ramón Méndez-Galain and Nicolás Wschebor

  • Instituto de Física, Facultad de Ingeniería, J.H.y Reissig 565, 11000 Montevideo, Uruguay

  • *Electronic address: blaizot@ect.it
  • Electronic address: mendezg@fing.edu.uy
  • Electronic address: nicws@fing.edu.uy

See Also

Nonperturbative renormalization group and momentum dependence of n-point functions. I

Jean-Paul Blaizot, Ramón Méndez-Galain, and Nicolás Wschebor
Phys. Rev. E 74, 051116 (2006)

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Vol. 74, Iss. 5 — November 2006

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