scholarly journals Local potential approximation for the renormalization group flow of fermionic field theories

2013 ◽  
Vol 88 (6) ◽  
Author(s):  
A. Jakovác ◽  
A. Patkós
Keyword(s):  
Renormalization Group ◽  
Local Potential ◽  
Field Theories ◽  
Renormalization Group Flow ◽  
Fermionic Field ◽  
Potential Approximation ◽  
Local Potential Approximation ◽  
Group Flow

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.

RENORMALIZATION GROUP AND VIRASORO CONSTRAINTS IN LIOUVILLE FIELD THEORIES

1991 ◽  
Vol 06 (25) ◽  
pp. 2289-2300 ◽  
Author(s):  
TAKAHIRO KUBOTA ◽  
YI-XIN CHENG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Matrix Models ◽  
Liouville Theory ◽  
Target Space ◽  
Field Theories ◽  
Renormalization Group Flow ◽  
Virasoro Constraints ◽  
Group Flow ◽  
Matter Fields

The idea of Wilson's renormalization group is applied to the 2-dimensional Liouville theory coupled to matter fields. The Virasoro structures including those of Liouville field are explicitly derived at the fixed point of the renormalization group flow. The Virasoro operators are transformed into another set of Virasoro operators acting in the target space and it is argued that the latter could be interpreted as those discovered recently in matrix models.

scholarly journals The Effectiveness of the Local Potential Approximation in the Wegner-Houghton Renormalization Group

1996 ◽  
Vol 95 (2) ◽  
pp. 409-420 ◽  
Author(s):  
K.-I. Aoki ◽  
K. Morikawa ◽  
W. Souma ◽  
J.-I. Sumi ◽  
H. Terao
Keyword(s):  
Renormalization Group ◽  
Local Potential ◽  
Potential Approximation ◽  
Local Potential Approximation
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