scholarly journals INVARIANT FORMULATION OF THE FUNCTIONAL RENORMALIZATION GROUP METHOD FOR U(n)×U(n) SYMMETRIC MATRIX MODELS

2012 ◽  
Vol 27 (36) ◽  
pp. 1250212 ◽  
Author(s):  
A. PATKÓS
Keyword(s):  
Renormalization Group ◽  
Symmetric Matrix ◽  
The Other ◽  
Group Method ◽  
Renormalization Group Method ◽  
Potential Approximation ◽  
Functional Renormalization Group ◽  
Local Potential Approximation ◽  
Invariant Formulation ◽  
Symmetric Theory

The Local Potential Approximation (LPA) to the Wetterich-equation is formulated explicitly in terms of operators, which are invariant under the U (n)× U (n) symmetry group. Complete formulas are presented for the two-flavor ( U (2)× U (2)) case. The same approach leads to a unique natural truncation of the functional driving the renormalization flow of the potential of the three-flavor case ( U (3)× U (3)). The procedure applied to the SU (3)× SU (3) symmetric theory, results in an equation, which potentially allows an RG-investigation of the effect of the 't Hooft term representing the U A(1) anomaly, disentangled from the other operators.

scholarly journals Optimized regulator for the quantized anharmonic oscillator

2015 ◽  
Vol 30 (12) ◽  
pp. 1550058 ◽  
Author(s):  
J. Kovacs ◽  
S. Nagy ◽  
K. Sailer
Keyword(s):  
Renormalization Group ◽  
Ground State ◽  
Evolution Equations ◽  
Energy Gap ◽  
Anharmonic Oscillator ◽  
Group Method ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
First Excited State ◽  
Symmetric Phase

The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used which includes various types of regulators as limiting cases. It was found that the value of the energy gap depends on the regulator parameters. We argue that the optimization based on the disappearance of the false, broken symmetric phase of the model leads to the Litim's regulator. The least sensitivity on the regulator parameters leads, however, to an IR regulator being somewhat different of the Litim's one, but it can be described as a perturbatively improved, or generalized Litim's regulator and provides analytic evolution equations, too.

COUNTING STATISTICS OF NONEQUILIBRIUM TUNNELING PROCESS USING FUNCTIONAL RENORMALIZATION GROUP

2010 ◽  
Vol 24 (05) ◽  
pp. 575-585 ◽  
Author(s):  
QING-QIANG XU ◽  
BEN-LING GAO ◽  
SHI-JIE XIONG
Keyword(s):  
Renormalization Group ◽  
Charge Transfer ◽  
Quantum Dot ◽  
Group Method ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Nonequilibrium Transport ◽  
Cumulant Generating Function ◽  
Full Counting Statistics ◽  
Counting Statistics

We develop a scheme to investigate the flux of nonequilibrium transport based on the full counting statistics and nonequilibrium functional renormalization group method. As an illustrative example, we study the charge transfer in the system of an interacting quantum dot connected to two noninteracting reservoirs via tunneling. Within the lowest approximation in functional renormalization group, we obtain the cumulant generating function analytically.

scholarly journals STRUCTURE OF THE BROKEN PHASE OF THE SINE-GORDON MODEL USING FUNCTIONAL RENORMALIZATION

2012 ◽  
Vol 27 (03n04) ◽  
pp. 1250014 ◽  
Author(s):  
V. PANGON
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Fourier Series ◽  
Fixed Points ◽  
Potential Approximation ◽  
Functional Renormalization Group ◽  
Strongly Coupled ◽  
Local Potential Approximation ◽  
Average Action ◽  
Sine Gordon Model

We study in this paper the sine-Gordon model using functional renormalization group at local potential approximation using different renormalization group (RG) schemes. In d = 2, using Wegner–Houghton RG we demonstrate that the location of the phase boundary is entirely driven by the relative position to the Coleman fixed point even for strongly coupled bare theories. We show the existence of a set of IR fixed points in the broken phase that are reached independently of the bare coupling. The bad convergence of the Fourier series in the broken phase is discussed and we demonstrate that these fixed points can be found only using a global resolution of the effective potential. We then introduce the methodology for the use of average action method where the regulator breaks periodicity and show that it provides the same conclusions for various regulators. The behavior of the model is then discussed in d≠2 and the absence of the previous fixed points is interpreted.

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.

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