scholarly journals Towards an accurate determination of the critical exponents with the renormalization group flow equations

2001 ◽  
Vol 504 (1-2) ◽  
pp. 181-187 ◽  
Author(s):  
A. Bonanno ◽  
D. Zappalà
Keyword(s):  
Renormalization Group ◽  
Critical Exponents ◽  
Accurate Determination ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Group Flow

scholarly journals Renormalization group flow equations with full momentum dependence

2011 ◽  
Vol 369 (1946) ◽  
pp. 2735-2758 ◽  
Author(s):  
Jean-Paul Blaizot
Keyword(s):  
Renormalization Group ◽  
Einstein Condensation ◽  
Momentum Dependence ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Bose Einstein ◽  
Exact Renormalization Group ◽  
Group Flow ◽  
Truncation Of The Hierarchy

After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the n -point functions. Applications are then briefly presented, to critical O ( N ) models, to Bose–Einstein condensation and to finite-temperature field theory.

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.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals Block diagonalization using similarity renormalization group flow equations

2008 ◽  
Vol 77 (3) ◽  
Author(s):  
E. Anderson ◽  
S. K. Bogner ◽  
R. J. Furnstahl ◽  
E. D. Jurgenson ◽  
R. J. Perry ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Block Diagonalization ◽  
Renormalization Group Flow ◽  
Similarity Renormalization Group ◽  
Flow Equations ◽  
Group Flow

CRITICAL EXPONENTS, SCALING LAW, UNIVERSALITY AND RENORMALIZATION GROUP FLOW IN STRONG COUPLING QED

1991 ◽  
Vol 06 (30) ◽  
pp. 5447-5466 ◽  
Author(s):  
KEI-ICHI KONDO
Keyword(s):  
Renormalization Group ◽  
Critical Exponents ◽  
Scaling Law ◽  
Mean Field ◽  
Universality Class ◽  
Dyson Equation ◽  
Renormalization Group Flow ◽  
Strongly Coupled ◽  
Renormalized Charge ◽  
Group Flow

The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

scholarly journals SYMPLECTIC GEOMETRY AND HAMILTONIAN FLOW OF THE RENORMALIZATION GROUP EQUATION

1995 ◽  
Vol 10 (18) ◽  
pp. 2703-2732 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Poisson Bracket ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Identity Operator ◽  
Group Equation ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Group Flow

It is argued that renormalization group flow can be interpreted as a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate “momenta,” which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum operator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential in the flow equations. The evolution of any quantity, such as N-point Green functions, under renormalization group flow can be obtained from its Poisson bracket with the Hamiltonian. Ward identities can be represented as constants of the motion which act as symmetry generators on the phase space via the Poisson bracket structure.

scholarly journals Solutions of renormalization-group flow equations with full momentum dependence

2009 ◽  
Vol 80 (3) ◽  
Author(s):  
F. Benitez ◽  
J.-P. Blaizot ◽  
H. Chaté ◽  
B. Delamotte ◽  
R. Méndez-Galain ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Momentum Dependence ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Group Flow
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