Critical exponents from optimised renormalisation group flows

Abstract

Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared regularisation. The Wilson-Fisher fixed point in d=3 is studied using an optimised flow. We compute critical exponents and subleading corrections-to-scaling to high accuracy from the eigenvalues of the stability matrix at criticality for all N. We establish that the optimisation is responsible for the rapid convergence of the flow and polynomial truncations thereof. The scheme dependence of the leading critical exponent is analysed. For all N > 0, it is found that the leading exponent is bounded. The upper boundary is achieved for a Callan-Symanzik flow and corresponds, for all N, to the large-N limit. The lower boundary is achieved by the optimised flow and is closest to the physical value. We show the reliability of polynomial approximations, even to low orders, if they are accompanied by an appropriate choice for the regulator. Possible applications to other theories are outlined.

34 pages, 15 figures, revtex, to appear in NPB

References in corpus (6)

• Exact evolution equation for the effective potential
• Optimised Renormalisation Group Flows
• Mind The Gap
• Derivative expansion and renormalisation group flows
• Predictive power of renormalisation group flows: a comparison
• Proper time regulator and Renormalization Group flow

Cited by in corpus (165)

• Aspects of the Functional Renormalisation Group
• The nonperturbative functional renormalization group and its applications
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Fixed points of quantum gravity
• An Introduction to the Nonperturbative Renormalization Group
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Fundamentals of the Exact Renormalization Group
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• On the renormalization group flow of f(R)-gravity
• Further evidence for asymptotic safety of quantum gravity
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Renormalisation group and the Planck scale
• Chiral phase structure of QCD with many flavors
• Fixed points of quantum gravity in extra dimensions
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Boundary and Interface CFTs from the Conformal Bootstrap
• The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density
• A new method to solve the Non Perturbative Renormalization Group equations
• One force to rule them all: asymptotic safety of gravity with matter
• Physics searches at the LHC
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Asymptotic safety: a simple example
• Crumpling transition and flat phase of polymerized phantom membranes
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Generalized Parametrization Dependence in Quantum Gravity
• Non-equilibrium Functional Renormalization for Driven-Dissipative Bose-Einstein Condensation
• Quark-meson-diquark model for two-color QCD
• Completeness and consistency of renormalisation group flows
• Ising exponents from the functional renormalisation group
• Lectures on renormalization and asymptotic safety
• From Big Bang to Asymptotic de Sitter: Complete Cosmologies in a Quantum Gravity Framework
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Wilsonian flows and background fields
• Higher order quark-mesonic scattering processes and the phase structure of QCD
• The R^2 phase-diagram of QEG and its spectral dimension
• The QCD Phase Boundary from Quark-Gluon Dynamics
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• Critical behavior of Dirac fermions from perturbative renormalization
• Non-perturbative thermal flows and resummations
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Chiral Susceptibility in (2+1)-flavour QCD
• Critical behavior of the (2+1)-dimensional Thirring model
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Signatures of gravitational fixed points at the LHC
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Renormalization Group Flow in Scalar-Tensor Theories. II
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Background independent exact renormalization group for conformally reduced gravity
• Universal Aspects of QCD-like Theories
• Ising and Gross-Neveu model in next-to-leading order
• The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
• Scattering amplitudes in super-renormalizable gravity
• Critical behavior in spherical and hyperbolic spaces
• High-accuracy scaling exponents in the local potential approximation
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Universality and the Renormalisation Group
• Solving functional flow equations with pseudo-spectral methods
• Multi-meson Yukawa interactions at criticality
• Lorentz symmetry is relevant
• Multicritical behavior in models with two competing order parameters
• Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Thermodynamics of QCD low-energy models and the derivative expansion of the effective action
• Lee-Yang model from the functional renormalization group
• The Planck scale, the Higgs mass and scalar dark matter
• Computing the Effective Action with the Functional Renormalization Group
• On de Sitter solutions in asymptotically safe $f(R)$ theories
• Subleading critical exponents from the renormalisation group
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Infinite order quantum-gravitational correlations
• Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations
• The Functional Renormalization Group and O(4) scaling
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Global Wilson-Fisher fixed points
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Fixed Points of Quantum Gravity and the Renormalisation Group
• Fixed points and the spontaneous breaking of scale invariance
• Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas
• Shocks and quark-meson scatterings at large density
• Critical $O(N)$ models in the complex field plane
• Critical behavior of weakly interacting bosons: A functional renormalization group approach
• Optimization of field-dependent nonperturbative renormalization group flows
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Asymptotic safety of scalar field theories
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Scaling and superscaling solutions from the functional renormalization group
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Scaling functions for the O(4)-model in d=3 dimensions
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• Functional renormalization group with a compactly supported smooth regulator function
• Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group
• Finite-Size Scaling behavior in the O(4)-Model
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
• Functional renormalization group approach to the Yang-Lee edge singularity
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• Vanishing Beta Function curves from the Functional Renormalisation Group
• N=1 Wess Zumino Model in d=3 at zero and finite temperature
• Critical behavior of supersymmetric O(N) models in the large-N limit
• Onset of symmetry breaking by the functional RG method
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Bosonization and Functional Renormalization Group Approach in the Framework of QED_2
• Functional renormalization group approach to non-collinear magnets
• Spontaneous symmetry breaking and optimization of functional renormalization group
• Functional Renormalization and $\overline{\text{MS}}$
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group
• The flat phase of quantum polymerized membranes
• Phases of supersymmetric O(N) theories
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Momentum dependence of quantum critical Dirac systems
• Revisited functional renormalization group approach for random matrices in the large-$N$ limit
• (No) phase transition in tensorial group field theory
• On the 2-point function of the O(N) model
• Scaling relations and multicritical phenomena from Functional Renormalization
• The regulator dependence in the functional renormalization group: a quantitative explanation
• The ordered phase of $O(N)$ model within the Non-Perturbative Renormalization Group
• Sarma phase in relativistic and non-relativistic systems
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Structure of the broken phase of the sine-Gordon model using functional renormalization
• Functional flows for complex effective actions
• Critical Behavior and Dimension Crossover of Pion Superfluidity
• Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity
• Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
• Alternative flow equation for the functional renormalization group
• Towards Functional Flows for Hierarchical Models
• Dimensional reduction and its breakdown in the 3-dimensional long-range random field Ising model
• Critical behavior of the random-field Ising model with long-range interactions in one dimension
• Line of Fixed Points in Gross-Neveu Theories
• More about the Wilsonian analysis on the pionless NEFT
• Interplay of fixed points in scalar models
• Interplay Between Approximation Theory and Renormalization Group
• Correlation functions in the Non Perturbative Renormalization Group and field expansion
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Regulator scheme dependence of the chiral phase transition at high densities
• The Numerically Optimized Regulator and the Functional Renormalization Group
• Mass hierarchy in collective modes of pair-density-wave superconductors
• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Limit of vanishing regulator in the functional renormalization group
• Critical Fermions with Spontaneously Broken Scale Symmetry
• Asymptotic safety in the dark
• The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach
• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• Functional renormalization of N scalars with O(N) invariance
• Universality in long-range interacting systems: the effective dimension approach
• Renormalization group flow equations with full momentum dependence
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group
• Scale symmetry breaking and generation of mass at quantum critical points
• The local potential approximation in the background field formalism
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Phase structure of the $O(2)$ ghost model with higher-order gradient term
• A new functional RG flow: regulator-sourced 2PI versus average 1PI
• Fermion Mass Generation without Symmetry Breaking
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• One-loop functional RG flow of scalar theory with electroweak symmetry
• Universality in the exact renormalization group: comparison to perturbation theory
• Renormalisation Group for Gravity and Dimensional Reduction