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

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 ΔT_c, 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.