Solutions of renormalization group flow equations with full momentum dependence

Abstract

We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow equations obtained within this scheme, and compute the two-point functions of the O(N) theories at criticality, in two and three dimensions. Excellent results are obtained for both universal and non-universal quantities at modest numerical cost.

4 pages, 1 figure

References in corpus (10)

• Exact evolution equation for the effective potential
• The critical exponents of the superfluid transition in He4
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Non-perturbative fixed point in a non-equilibrium phase transition
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• On the 2-point function of the O(N) model
• Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions

Cited by in corpus (79)

• The nonperturbative functional renormalization group and its applications
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
• Asymptotic safety: a simple example
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Ising exponents from the functional renormalisation group
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Critical behavior of Dirac fermions from perturbative renormalization
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• Ultracold atoms and the Functional Renormalization Group
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Renormalization: an advanced overview
• Ising and Gross-Neveu model in next-to-leading order
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
• Solving functional flow equations with pseudo-spectral methods
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Thermodynamics of QCD low-energy models and the derivative expansion of the effective action
• Infrared behavior in systems with a broken continuous symmetry: classical O(N) model vs interacting bosons
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations
• The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
• Nonlocal effective average action approach to crystalline phantom membranes
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
• Functional renormalization group at finite density and Bose condensation
• Vanishing Beta Function curves from the Functional Renormalisation Group
• N=1 Wess Zumino Model in d=3 at zero and finite temperature
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Thermodynamics of a Bose gas near the superfluid--Mott-insulator transition
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• Phases of supersymmetric O(N) theories
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Momentum dependence of quantum critical Dirac systems
• Kardar-Parisi-Zhang Equation with temporally correlated noise: a non-perturbative renormalization group approach
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• The ordered phase of $O(N)$ model within the Non-Perturbative Renormalization Group
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Some exact results in branching and annihilating random walks
• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Interplay of fixed points in scalar models
• Degeneracy induced scaling of the correlation length for periodic models
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• On the nature of the Schmid transition in a resistively shunted Josephson junction
• Critical $O(2)$ field theory near six dimensions beyond one loop
• Enhancement of field renormalization in scalar theories via functional renormalization group
• The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach
• Effective average action based approach to correlation functions at finite momenta
• FlowPy - a numerical solver for functional renormalization group equations
• Renormalization group flow equations with full momentum dependence
• First-order phase transitions in spinor Bose gases and frustrated magnets
• Interplay of topology and geometry in frustrated 2d Heisenberg magnets
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Quantum interface unbinding transitions
• Functional renormalisation group approach to the finite-temperature Bose polaron
• Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• 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
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group