Europhys. Lett.
Volume 72, Number 5, December 2005
Page(s) 705 - 711
Section General
Published online 04 November 2005
Europhys. Lett., 72 (5), pp. 705-711 (2005)
DOI: 10.1209/epl/i2005-10318-5

Non-Perturbative Renormalization Group calculation of the transition temperature of the weakly interacting Bose gas

J.-P. Blaizot1, R. Méndez Galain2 and N. Wschebor2

1  ECT*, Villa Tambosi - Strada delle Tabarelle 286, I-38050 Villazzano (TN), Italy
2  Instituto de Física, Facultad de Ingeniería - J.H.y Reissig 565 11000 Montevideo, Uruguay

received 29 July 2005; accepted in final form 10 October 2005
published online 4 November 2005

We present a new approximation scheme to solve the Non-Perturbative Renormalization Group equations and obtain the full momentum dependence of n-point functions. The core of the method consists in deriving approximate flow equations that are then solved exactly. The results thus obtained can next be improved through an iteration procedure. The approximations proposed in this paper lead to approximate equations that are accurate both in the perturbative and the scaling regimes. The scheme is tested with the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momentum scales. The leading-order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result.

03.75.Nt - Other Bose-Einstein condensation phenomena.
05.10.Cc - Renormalization group methods.
05.30.Jp - Boson systems.

© EDP Sciences 2005