The Exact Renormalisation Group and Approximate Solutions

Abstract

We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\lambda {\phi }^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.

49 pages (with figures), Plain TeX, uses psfig, 7 postscript figures appended as uuencoded compressed tar file, SHEP 92/93-27, CERN-TH.6977/93, Note Added with more complete comparison to earlier work

References in corpus (2)

• Critical Exponents from the Effective Average Action
• Renormalization of Tamm-Dancoff Integral Equations

Cited by in corpus (729)

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• Fluctuation-induced higher-derivative couplings and infrared dynamics of the Quark-Meson-Diquark Model
• Critical Fermions with Spontaneously Broken Scale Symmetry
• Interplay between chiral dynamics and repulsive interactions
• Non-Analytic Vertex Renormalization of a Bose Gas at Finite Temperature
• Steps towards Lorentzian quantum gravity with causal sets
• Asymptotic safety in the dark
• Renormalization group properties of the conformal mode of a torus
• The Inverse of Exact Renormalization Group Flows as Statistical Inference
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• N=1* model and glueball superpotential from Renormalization-Group-improved perturbation theory
• Fermi surface renormalization and confinement in two coupled metallic chains
• On the Running of Gauge Couplings in String Theory
• Renormalization-Group flow for the field strength in scalar self-interacting theories
• Critical line of the ${\Phi }^4$ theory on a simple cubic lattice in the local potential approximation
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Functional Callan-Symanzik Equation for the Coulomb Gas
• Computing First-Passage Times with the Functional Renormalisation Group
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method
• Spatio-temporal correlation functions in scalar turbulence from functional renormalization group
• Renormalization of QCD_2
• Structural aspects of FRG in quantum tunnelling computations
• Scaling Laws in the Cosmic Structure and Renormalization Group
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Exact Renormalization Group and Sine Gordon Theory
• The continuum limit of quantum gravity at first order in perturbation theory
• COMBINING MCRG AND FOURIER ACCELERATED LANGEVIN ALGORITHM
• Effective average action based approach to correlation functions at finite momenta
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Effective low-energy Hamiltonians for interacting nanostructures
• Five-dimensional scale-dependent black holes with constant curvature and Solv horizons
• Gauge Invariant Cutoff QED
• Gravitational Collapse in Scale-Dependent Gravity
• The effects of running gravitational coupling on three dimensional black holes
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
• Fine-tuning and vacuum stability in Wilsonian effective action
• The inviscid fixed point of the multi-dimensional Burgers-KPZ equation
• Condensate density of interacting bosons: a functional renormalization group approach
• Hierarchical Reference Theory of critical fluids in disordered porous media
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• The exact renormalization group in Astrophysics
• Thermal behavior of effective U_A(1) anomaly couplings in reflection of higher topological sectors
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• The epsilon-expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature
• Renormalization group flow for fermions into antiferromagnetically ordered phases: Method and mean-field models
• Wilson Action for the $O(N)$ Model
• Monte Carlo and Renormalization Group Effective Potentials in Scalar Field Theories
• Long-Range and Many-Body Effects in Coagulation Processes
• Keldysh functional renormalization group for electronic properties of graphene
• Correlated Worldline theory: Structure and Consistency
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
• Renormalization group flow equations with full momentum dependence
• Effective scalar potential in asymptotically safe quantum gravity
• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• The continuum limit of quantum gravity at second order in perturbation theory
• Space of non-Fermi liquids
• Background Field Functional Renormalization Group for Absorbing State Phase Transitions
• The large system asymptotics of persistent currents in mesoscopic quantum rings
• Exact renormalization group approach to a nonlinear diffusion equation
• Competing many-body instabilities in two-dimensional dipolar Fermi gases
• Vainshtein in the UV and a Wilsonian analysis of derivatively coupled scalars
• Field dependence of the Yukawa coupling in the three flavor quark-meson model
• Interplay of topology and geometry in frustrated 2d Heisenberg magnets
• Solving the QCD non-perturbative flow equation as a partial differential equation and its application to the dynamical chiral symmetry breaking
• Lectures in Quantum Gravity
• Link between New Versions of the Hierarchical Reference Theory of Liquids and of the Non Perturbative Renormalization Group in Statistical Field Theory
• A Renormalization-Group Study of Interacting Bose-Einstein condensates: Absence of the Bogoliubov Mode below Four ($T>0$) and Three ($T=0$) Dimensions
• Isotropic Lifshitz Scaling in four dimensions
• A technique for natural gauge boson masses
• Spectral functions from the functional renormalization group at finite temperature and density
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• The Functional Renormalization Group for Zero-Dimensional Quantum Systems in and out of Equilibrium
• Flowing bosonization in the nonperturbative functional renormalization-group approach
• A Comment on the Path Integral Approach to Cosmological Perturbation Theory
• High temperature phase of QCD
• Stochastic dynamics for Group Field Theories
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• Regular black hole from a confined spin connection in Poincare gauge gravity
• On the low-energy spectrum of an SU(2) gauge theory with dynamical fermions
• Wilsonian Renormalization Group Approach to $\mathcal{N}=2$ Supersymmetric Sigma Models
• Wegner-Houghton equation in low dimensions
• Peccei-Quinn Symmetry Breaking via Asymptotically Safe Dynamical Scalegenesis: A Walking Axicolor and Axion
• Renormalisation Group determination of scalar mass bounds in a simple Yukawa-model
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
• Structure of Exact Renormalization Group Equations for field theory
• Stability of Fine Tuned Hierarchies in Strongly Coupled Chiral Models
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• The local potential approximation in the background field formalism
• Scale symmetry breaking and generation of mass at quantum critical points
• A New Class of Conformal Field Theories with Anomalous Dimensions
• Second order functional renormalization group approach to one-dimensional systems in real and momentum space
• Exact Renormalization Group : A New Method for Blocking the Action
• On the phase structure of extra-dimensional gauge theories with fermions
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Quantum-classical transition in the Caldeira-Leggett model
• Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics
• Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Pseudo-Periodic Natural Higgs Inflation
• Linked-cluster Tamm-Dancoff Field Theory
• A Rigorous Derivation of the Functional Renormalisation Group Equation
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Non-perturbative solution of metastable scalar models
• Suppression of proton decay in quantum gravity
• Scaling violation and the magnetic equation of state in chiral models
• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons
• Renormalization-Group Running Induced Cosmic Inflation
• Functional Renormalization-Group Analysis of Luttinger Liquids with Impurities
• Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension
• Exact renormalization group for wave functionals
• Scaling solutions for asymptotically free quantum gravity
• The continuum limit of the conformal sector at second order in perturbation theory
• Flow equation of functional renormalization group for three-body scattering problems
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Bulk Gauge Fields and Holographic RG from Exact RG
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
• A new functional RG flow: regulator-sourced 2PI versus average 1PI
• Functional renormalization group approach to interacting three-dimensional Weyl semimetals
• Critical line of the ${\Phi }^4$ scalar field theory on a 4D cubic lattice in the local potential approximation
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Time Evolution and Thermal Renormalization Group Flow in Cosmology
• Non-perturbative quantum Galileon in the exact renormalization group
• Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk
• Aspects of quantum gravity
• Analytical Methods and Field Theory for Disordered Systems
• New renormalization group study of the 3-state Potts model and related statistical models
• Cutoff Function in Holographic RG Flow
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas
• Non-analytic magnetic field dependence of quasi-particle properties of two-dimensional metals
• Kinetics of the chiral phase transition in a quark-meson $\sigma$-model
• Functional Renormalisation Group for Brownian Motion I: The Effective Equations of Motion
• Lectures on Naturalness, String Landscape and Multiverse
• Non-renormalization for planar Wess-Zumino model
• Comment on "The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization"
• Fermionic Functional Renormalization Group Approach to Bose-Einstein Condensation of Dimers
• Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion
• A control on quantum fluctuations in 2+1 dimensions
• Stabilizing dark matter with quantum scale symmetry
• An Extension of Pohlmeyer's Theorem
• Vacuum Energy and Renormalization of the Field-Independent Term
• Background Effective Action with Nonlinear Massive Gauge Fixing
• Spontaneous symmetry breaking with Wilson renormalization group
• Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation
• The generating functional of correlation functions as a high momentum limit of a Wilson action
• Renormalization Group Flow Equations for the Sigma Model
• Exact renormalization group approach in scalar and fermionic theories
• Testing the assumptions of the Effective Field Theory of Large-Scale Structure
• Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking
• Flows of multicomponent scalar models with U(1) gauge symmetry
• Fine-tuning and the Wilson renormalization group
• Functional renormalization group study of a four-fermion model with $CP$ violation
• A Renormalization-Group Study of Interacting Bose-Einstein Condensates: II. Anomalous Dimension $\eta$ for $d\lesssim 4$ at Finite Temperatures
• Coulomb Gas and Sine-Gordon Model in Arbitrary Dimension
• Exact effective action for the O(N) vector model in the large N limit
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Functional renormalization group for signal detection and stochastic ergodicity breaking
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• Renormalization Flow of Nonlinear Electrodynamics
• Renormalization of the bilocal sine-Gordon model
• Reformulations of Yang-Mills Theories with Space-time Tensor Fields
• Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model
• N=1* model superpotential revisited (IR behaviour of N=4 limit)
• Fermion Mass Generation without Symmetry Breaking
• The Conformal Anomaly and a new Exact RG
• A functional renormalization group approach to electronic structure calculations for systems without translational symmetry
• A basis of the gradient flow exact renormalization group for gauge theory
• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Finite Cutoff CFT's and Composite Operators
• Perturbative versus Non-Perturbative Renormalization
• One-loop functional RG flow of scalar theory with electroweak symmetry
• Asymptotic safety and quantum gravity amplitudes
• Interacting two-particle states in the symmetric phase of the chiral Nambu--Jona-Lasinio model
• A Universe from a Lagrangian Fixed Point
• Cosmology from Strong Interactions
• Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
• Momentum-dependence in the infinitesimal Wilsonian renormalization group
• Thermal and Quantum Phase Transitions of the ${\varphi }^4$ Model
• QCD chiral phase diagram from weak functional renormalization group
• On the wave function renormalization for Wilson actions and their 1PI actions
• Universality in the exact renormalization group: comparison to perturbation theory
• Indications against dynamical CPT symmetry restoration in quantum gravity
• A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots
• Vertex functions and their flow equations from the 2PI effective action
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Differential equation for partition functions and a duality pseudo-forest
• On the reconstruction problem in Quantum Gravity
• Functional Renormalization Group Flows and Gauge Consistency in QED
• Functional Renormalization Group Approach for Signal Detection
• On Functional and Holographic Renormalization Group Methods in Stochastic Theory of Turbulence
• Scaling Behaviors in Active Model B+ via the Functional Renormalization Group
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• A renormalization group improved computation of correlation functions in theories with non-trivial phase diagram
• Mean field flow equations and asymptotically free scalar fields
• Thermal RG Flow of AS Quantum Gravity
• Renormalization group approach to the elastic properties of graphene bilayers
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Renormalisation of non-differentiable potentials
• Three dimensional conformal sigma models
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation
• The $\theta$-vacuum from functional renormalisation
• Weak coupling theory of nickel-based 327 superconductors
• The exact renormalization group and dimensional regularization
• Functional Renormalization for Signal Detection: Dimensional Analysis and Dimensional Phase Transition for Nearly Continuous Spectra Effective Field Theory
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions
• Constructing CFTs from AdS flows
• Self-consistent renormalization group flow
• Surface Functional Renormalization Group for Layered Quantum Materials
• Vacuum polarization in Uranium
• Functional renormalization group for non-Hermitian and $\mathcal{P}\mathcal{T}$-symmetric systems
• Emergence of dynamical tensor fields in composite models of gravity
• An Alternative to Exact Renormalization and Cosmological Solutions in String Theory
• Non-Perturbative $S$-matrix Renormalization
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• $SO(1,d+1)$ symmetry of the Exact RG equation
• Wilsonian Renormalization Group In The Functional Nonperturbative Approach
• Geodesics in Quantum Gravity
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature
• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
• Higher-derivative four-dimensional sine-Gordon model
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas
• Holographic RG and Exact RG in O(N) Model
• Functional renormalization group approach to the singlet-triplet transition in quantum dots
• Multi-Regulator Functional Renormalization Group for Many-Fermion Systems
• Functional Renormalization Group for fermions on a one dimensional lattice at arbitrary filling
• Journey from the Wilson exact RG towards the Wegner-Morris Fokker-Planck RG and the Carosso field-coarsening via Langevin stochastic processes
• Functional renormalization group approach to phonon modified criticality: anomalous dimension of strain and non-analytic corrections to Hooke's law
• Novel Approaches to Renormalization Group Transformations in the Continuum and on the Lattice
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group
• Naturalness, Wilsonian Renormalization, and "Fundamental Parameters" in Quantum Field Theory
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems