scholarly journals Cosmological functional renormalization group, extended Galilean invariance, and approximate solutions to the flow equations

2022 ◽  
Vol 105 (2) ◽  
Author(s):  
Alaric Erschfeld ◽  
Stefan Floerchinger
Keyword(s):  
Renormalization Group ◽  
Approximate Solutions ◽  
Galilean Invariance ◽  
Functional Renormalization Group ◽  
Flow Equations

scholarly journals THE EXACT RENORMALIZATION GROUP AND APPROXIMATE SOLUTIONS

1994 ◽  
Vol 09 (14) ◽  
pp. 2411-2449 ◽  
Author(s):  
TIM R. MORRIS
Keyword(s):  
Renormalization Group ◽  
Approximation Scheme ◽  
Approximate Solutions ◽  
Flow Equations ◽  
Qualitative And Quantitative ◽  
Nonperturbative Approximation ◽  
Exact Renormalization Group ◽  
Cactus Approximation ◽  
Sharp Cutoff ◽  
The Continuum

We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff Green’s functions are given. A promising nonperturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in “irrelevancy” of operators. We illustrate with two simple models of four-dimensional λφ4 theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.

scholarly journals A COMPARED ANALYSIS OF THE SUSCEPTIBILITY IN THE O(N) THEORY

2013 ◽  
Vol 28 (17) ◽  
pp. 1350078 ◽  
Author(s):  
VINCENZO BRANCHINA ◽  
EMANUELE MESSINA ◽  
DARIO ZAPPALÀ
Keyword(s):  
Renormalization Group ◽  
Numerical Analysis ◽  
Effective Potential ◽  
Renormalization Group Flow ◽  
Potential Approximation ◽  
Functional Renormalization Group ◽  
Flow Equations ◽  
Large N ◽  
Local Potential Approximation ◽  
Group Flow

The longitudinal susceptibility χL of the O(N) theory in the broken phase is analyzed by means of three different approaches, namely the leading contribution of the 1/N expansion, the Functional Renormalization Group flow in the Local Potential approximation and the improved effective potential via the Callan–Symanzik equations, properly extended to d = 4 dimensions through the expansion in powers of ϵ = 4-d. The findings of the three approaches are compared and their agreement in the large N limit is shown. The numerical analysis of the Functional Renormalization Group flow equations at small N supports the vanishing of [Formula: see text] in d = 3 and d = 3.5 but is not conclusive in d = 4, where we have to resort to the Callan–Smanzik approach. At finite N as well as in the limit N→∞, we find that [Formula: see text] vanishes with J as Jϵ/2 for ϵ> 0 and as ( ln (J))-1 in d = 4.

scholarly journals RG flows of integrable σ-models and the twist function

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
François Delduc ◽  
Sylvain Lacroix ◽  
Konstantinos Sfetsos ◽  
Konstantinos Siampos
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Rational Function ◽  
Integrable Model ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Non Linear ◽  
Group Flow

Abstract In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

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