Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group

Abstract

We compute the critical exponents $\nu$, $\eta$ and $\omega$ of $O(N)$ models for various values of $N$ by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted $\mathcal{O}({\partial }^4)$]. We analyze the behavior of this approximation scheme at successive orders and observe an apparent convergence with a small parameter -- typically between $1/9$ and $1/4$ -- compatible with previous studies in the Ising case. This allows us to give well-grounded error bars. We obtain a determination of critical exponents with a precision which is similar or better than those obtained by most field theoretical techniques. We also reach a better precision than Monte-Carlo simulations in some physically relevant situations. In the $O(2)$ case, where there is a longstanding controversy between Monte-Carlo estimates and experiments for the specific heat exponent $\alpha$, our results are compatible with those of Monte-Carlo but clearly exclude experimental values.

References in corpus (60)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Critical Exponents of the N-vector model
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• An Introduction to the Nonperturbative Renormalization Group
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Critical Exponents from the Effective Average Action
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Derivative Expansion of the Exact Renormalization Group
• Bootstrapping Mixed Correlators in the 3D Ising Model
• The critical exponents of the superfluid transition in He4
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Critical exponents from optimised renormalisation group flows
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Bootstrapping the O(N) Archipelago
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
• A new method to solve the Non Perturbative Renormalization Group equations
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Numbers and Functions in Quantum Field Theory
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Monte Carlo study of an improved clock model in three dimensions
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Solutions of renormalization group flow equations with full momentum dependence
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Large N and the renormalization group
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Solving functional flow equations with pseudo-spectral methods
• Momentum Scale Expansion of Sharp Cutoff Flow Equations
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Convergence of derivative expansions of the renormalization group
• Equivalence of Local Potential Approximations
• Scale-free Monte Carlo method for calculating the critical exponent $\gamma$ of self-avoiding walks
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory
• Equation of state near the endpoint of the critical line
• Field Theories for Loop-Erased Random Walks
• The critical equation of state of the three-dimensional O(N) universality class: N>4
• Trace anomaly and infrared cutoffs
• Exact enumeration of self-avoiding walks on BCC and FCC lattices
• Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric ${\varphi }^4$ theory with $n\to -2$ and loop-erased random walks
• Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
• On Functional Representations of the Conformal Algebra
• A Conformal Fixed-Point Equation for the Effective Average Action
• Conformal invariance and vector operators in the $O(N)$ model
• Vortex-loop calculation of the specific heat of superfluid ${}^4$He under pressure
• High-precision Monte Carlo study of the three-dimensional XY model on GPU

Cited by in corpus (67)

• The nonperturbative functional renormalization group and its applications
• Coherent and dissipative dynamics at quantum phase transitions
• QCD at finite temperature and density within the fRG approach: An overview
• The critical O(N) CFT: Methods and conformal data
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Shocks and quark-meson scatterings at large density
• Functional renormalisation group for turbulence
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Soft modes in hot QCD matter
• Numerical RG-time integration of the effective potential: Analysis and Benchmark
• Lessons from conformally reduced quantum gravity
• Functional Renormalization and $\overline{\text{MS}}$
• The flat phase of polymerized membranes at two-loop order
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• The regulator dependence in the functional renormalization group: a quantitative explanation
• Continued functions and perturbation series: Simple tools for convergence of diverging series in $O(n)$-symmetric ${\varphi }^4$ field theory at weak coupling limit
• Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram
• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
• Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
• The $\lambda$-point anomaly in view of the seven-loop Hypergeometric resummation for the critical exponent $\nu$ of the $O(2)$ ${\varphi }^4$ model
• Regulator scheme dependence of the chiral phase transition at high densities
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• Limit of vanishing regulator in the functional renormalization group
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Fluctuation-induced higher-derivative couplings and infrared dynamics of the Quark-Meson-Diquark Model
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Flowing bosonization in the nonperturbative functional renormalization-group approach
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Corrections to scaling in the 3D Ising model: a comparison between MC and MCRG results
• Continued functions and Borel-Leroy transformation: Resummation of six-loop ε-expansions from different universality classes
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion
• Quantum Phases and Spin Liquid Properties of 1T-TaS2
• 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
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Critical Exponents of the O(N)-symmetric ${\varphi }^4$ Model from the \boldmath{\large{ ${\epsilon }^7$}} Hypergeometric-Meijer Resummation
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Constraint effective action and critical correlation functions at fixed magnetization
• Finite-Size Scaling of the majority-voter model above the upper critical dimension
• Superfluidity in multicomponent fermions via the functional renormalization group
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group
• Stability of universal properties against perturbations of the Markov Chain Monte Carlo algorithm
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Low-temperature behavior of the $O(N)$ models below two dimensions