Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-12-28
Phys.Rev.E74:051116,2006
Physics
High Energy Physics
High Energy Physics - Theory
48 pages, 15 figures A few minor corrections. A reference added
Scientific paper
10.1103/PhysRevE.74.051116
We present an approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of the $n$-point functions. It is based on an iterative procedure where, in a first step, an initial ansatz for the $n$-point functions is constructed by solving approximate flow equations derived from well motivated approximations. These approximations exploit the derivative expansion and the decoupling of high momentum modes. The method is applied to the O($N$) model. In leading order, the self energy is already accurate both in the perturbative and the scaling regimes. A stringent test is provided by the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is particularly sensitive to all momentum scales. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%.
Blaizot Jean Paul
Mendez-Galain Ramon
Wschebor Nicolas
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