Correlation functions in the Non Perturbative Renormalization Group and field expansion

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 $\eta$ by as much as 60%. However, if one goes to high order truncations the procedure seems to converge rapidly.

20 pages, 6 figures. Minor changes. Version to be published in EPJ B

References in corpus (23)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Critical Exponents of the N-vector model
• Optimisation of the exact renormalisation group
• Exact Renormalization Group Equations. An Introductory Review
• Critical Exponents from the Effective Average Action
• Flow Equations for N Point Functions and Bound States
• Derivative Expansion of the Exact Renormalization Group
• The transition temperature of the dilute interacting Bose gas
• Critical exponents from optimised renormalisation group flows
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• On Truncations of the Exact Renormalization Group
• A new method to solve the Non Perturbative Renormalization Group equations
• Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction
• Evolution Equations for the Quark-Meson Transition
• The Heavy Quark Potential from Wilson's Exact Renormalization Group
• Rapidly Converging Truncation Scheme of the Exact Renormalization Group
• Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• An analytical approximation scheme to two point boundary value problems of ordinary differential equations

Cited by in corpus (12)

• The nonperturbative functional renormalization group and its applications
• Fundamentals of the Exact Renormalization Group
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• On the 2-point function of the O(N) model
• Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy
• Non-perturbative renormalization-group approach to lattice models