2006/05/25 by Jean-Paul Blaizot, R. Méndez–Galain, Ramon Mendez-Galain +2 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Flow (mathematics) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field #Scalar field theory #cond-mat.other #hep-th
paper · pdf · doi:10.1140/epjb/e2007-00223-3
published as Eur.Phys.J.B58:297-309,2007 · 29 pages
arxiv created 2006/05/25 · openalex publication_date 2007/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.