RENORMALIZATION GROUP METHODS IN CONSTRUCTIVE FIELD THEORIES

2000 ◽  
Vol 14 (12n13) ◽  
pp. 1363-1398
Author(s):  
HIROSHI WATANABE
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Group Method ◽  
Coupling Region ◽  
Renormalization Group Analysis ◽  
New Approach ◽  
Group Methods ◽  
Technical Details ◽  
Hierarchical Approximation

Mathematical construction of quantum field theory is reviewed with emphasis on the conceptual structure of the construction and on the role of rigorous renormalization group analysis without technical details. After explaining a rigorous formulation of a renormalization group method in a weak coupling region, a new approach in a strong coupling region is proposed in the context of the hierarchical approximation. An idea of proving triviality in d≥4 dimensions utilizing this new proposal concludes this review.

RENORMALIZATION GROUP ANALYSIS OF A TWO-DIMENSIONAL INTERACTING ELECTRON SYSTEM

2001 ◽  
Vol 16 (11) ◽  
pp. 1889-1898
Author(s):  
WALTER METZNER
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Interaction Strength ◽  
Electron System ◽  
Flow Equation ◽  
Group Method ◽  
Model Parameters ◽  
Two Dimensional ◽  
Renormalization Group Analysis ◽  
Effective Interactions

We describe a Wick ordered functional renormalization group method for interacting Fermi systems, where the complete flow from the bare action of the microscopic model to the effective low-energy action is obtained from a differential flow equation. We apply this renormalization group approach to a prototypical two-dimensional lattice electron system, the Hubbard model on a square lattice. The flow equation for the effective interactions is evaluated numerically on 1-loop level. The effective interactions diverge at a finite energy scale which is exponentially small for small bare interactions. To analyze the nature of the instabilities signalled by the diverging interactions we compute the flow of the singlet superconducting susceptibilities for various pairing symmetries and also charge and spin density susceptibilities. Depending on the choice of the model parameters (hopping amplitudes, interaction strength and band-filling) we find antiferromagnetic order or d-wave superconductivity as leading symmetry breaking instability.

scholarly journals DOMAIN WALL RENORMALIZATION GROUP ANALYSIS OF TWO-DIMENSIONAL ISING MODEL

2009 ◽  
Vol 23 (18) ◽  
pp. 3739-3751 ◽  
Author(s):  
KEN-ICHI AOKI ◽  
TAMAO KOBAYASHI ◽  
HIROSHI TOMITA
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Domain Wall ◽  
Domain Walls ◽  
Group Analysis ◽  
Coarse Graining ◽  
Group Method ◽  
Two Dimensional ◽  
Renormalization Group Analysis ◽  
Renormalization Transformation

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-dimensional square lattice. For the lowest-order approximation with two-domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four-domain wall states.

scholarly journals Renormalization Group analysis of superradiant growth of self-interacting axion cloud

2021 ◽  
Author(s):  
Hidetoshi Omiya ◽  
Takuya Takahashi ◽  
Takahiro Tanaka
Keyword(s):  
Black Hole ◽  
Renormalization Group ◽  
Scalar Field ◽  
Group Analysis ◽  
Group Method ◽  
Renormalization Group Method ◽  
Renormalization Group Analysis ◽  
Rotating Black Hole ◽  
Realistic Situation ◽  
Light Scalar

Abstract There are strong interests in considering the ultra-light scalar field (especially axion) around a rapidly rotating black hole because of the possibility of observing a gravitational waves from axion condensate (axion cloud) around black hole. Motivated by this consideration, we study dynamics of ultra-light scalar field with self-interaction around a rapidly rotating black hole by the Renormalization group method. We found that for the relativistic cloud, saturation of the superradiant instability by the scattering of the axion due to the self-interaction does not occur in the weakly non-linear regime. This means that for the relativistic axion cloud, explosive phenomena called the Bosenova might happen in the realistic situation.

SCALING APPROACH TO THE ANISOTROPIC NONLOCAL KARDAR–PARISI–ZHANG EQUATION WITH SPATIALLY CORRELATED NOISE

2002 ◽  
Vol 16 (04) ◽  
pp. 563-569 ◽  
Author(s):  
GANG TANG ◽  
BENKUN MA
Keyword(s):  
Renormalization Group ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Group Analysis ◽  
Correlated Noise ◽  
Scaling Exponents ◽  
Coupling Region ◽  
Renormalization Group Analysis ◽  
Spatially Correlated ◽  
Spatially Correlated Noise

The scaling approach proposed by Hentschel and Family [Phys. Rev. Lett.66, 1982 (1991)] is generalized to the studies of the scaling of the anisotropic nonlocal Kardar–Parisi–Zhang equation with spatially correlated noise. The scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. The scaling exponents obtained in the weak-coupling region can well match the results of the dynamic renormalization-group analysis.

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