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 RENORMALIZATION GROUP FLOW EQUATIONS AND THE PHASE TRANSITION IN O(N)-MODELS

2001 ◽  
Vol 16 (23) ◽  
pp. 3823-3852 ◽  
Author(s):  
O. BOHR ◽  
B.-J. SCHAEFER ◽  
J. WAMBACH
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Flow Equations ◽  
Novel Approach ◽  
Self Consistent ◽  
Group Flow

We derive and solve numerically self-consistent flow equations for a general O(N)-symmetric effective potential without any polynomial truncation. The flow equations combined with a sort of a heat-kernel regularization are approximated in next-to-leading order of the derivative expansion. We investigate the method at finite temperature and study the nature of the phase transition in detail. Several beta functions, the Wilson–Fisher fixed point in three dimensions for various N are analyzed and various critical exponents β, ν, δ and η are independently calculated in order to emphasize the reliability of this novel approach.

scholarly journals The cubic fixed point at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Damon J. Binder
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Ising Models ◽  
Three Dimensions ◽  
Renormalization Group Flow ◽  
Conformal Bootstrap ◽  
Large N ◽  
Group Flow ◽  
3D Ising Model

Abstract By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

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 ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
Author(s):  
DARIO BENEDETTI ◽  
PEDRO F. MACHADO ◽  
FRANK SAUERESSIG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Group Flow ◽  
Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

Evolution of the Robertson–Walker metric under 2-loop renormalization group flow

2017 ◽  
Vol 26 (03) ◽  
pp. 1750021
Author(s):  
F. Hesamifard ◽  
M. M. Rezaii
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ricci Flow ◽  
Necessary Condition ◽  
Renormalization Group Flow ◽  
Twisted Product ◽  
Walker Metric ◽  
Group Flow

Here, we study the evolution of a Robertson–Walker (RW) metric under the Ricci flow and 2-loop renormalization group flow (RG-2 flow). We show that a RW metric is a fixed point of the Ricci flow and it is not a solution of the RG-2 flow. RG-2 flow is considered on a doubly twisted product metric with further assumptions and also we introduce a necessary condition for existence of the solution of RG-2 flow.

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

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.

Sign in / Sign up

Export Citation Format

Share Document