Correlation functions in the Non Perturbative Renormalization Group and field expansion

2007/04/30 by Diego Guerra, Diana Belkis Gómez Guerra, R. Méndez–Galain +3 · 3 citations
Mathematics · Physics and Astronomy · #Critical exponent #Criticality #Exponent #Geometry #High-Energy Particle Collisions Research #Mathematical physics #Mathematics #Momentum (technical analysis) #Non-perturbative #Order (exchange) #Particle physics theoretical and experimental studies #Phase transition #Physics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum gravity #Quantum mechanics #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field theory #Statistical physics #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1140/epjb/e2007-00296-x

published as Eur.Phys.J.B59:357-365,2007 · 20 pages, 6 figures. Minor changes. Version to be published in EPJ B

openalex publication_date 2007/10/01 · arxiv created 2007/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain n-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method recently introduced which includes simultaneously all vertices although approximating their momentum dependence. The study is performed using the self-energy of the tridimensional scalar model at criticality. At least in this example, low order truncations miss quantities as the critical exponent η by as much as 60%. However, if one goes to high order truncations the procedure seems to converge rapidly.

Citations

• The renormalization group and the ε expansion
• Evolution equations for the quark-meson transition
• Exact renormalization group equations: an introductory review
• Exact evolution equation for the effective potential
• Critical exponents from the effective average action
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Flow equations forN point functions and bound states
• Critical exponents of theN-vector model
• Nonperturbative Functional Renormalization Group for Random-Field Models: The Way Out of Dimensional Reduction
• Non-Perturbative Renormalization Group calculation of the transition temperature of the weakly interacting Bose gas
• Nonperturbative renormalization-group approach to frustrated magnets
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order \∂⁴

Cited by

• The nonperturbative functional renormalization group and its applications
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy