Exact solutions and residual regulator dependence in functional renormalisation group flows

Abstract

We construct exact solutions to the functional renormalisation group equation of the O(N) model and the Gross-Neveu model at large N for $2<d<4$, without specifying the form of the regulator. This allows to investigate which quantities are independent of the choice of regulator without being plagued by truncation artefacts. We find that only universal quantities, like critical exponents, and qualitative features, like the existence of a finite vacuum expectation value, are regulator-independent, whereas values of coupling constants are generically arbitrary. We also provide a general algorithm to construct a concrete operator basis for truncations in the derivative expansion and the Blaizot-Méndez-Wschebor scheme.

arXiv comment16 pages, 6+1 figures

References in corpus (68)

• 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
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• The nonperturbative functional renormalization group and its applications
• Optimisation of the exact renormalisation group
• Quantum Field Theory in the Large N Limit: a review
• An Introduction to the Nonperturbative Renormalization Group
• Introduction to the functional RG and applications to gauge theories
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• A new method to solve the Non Perturbative Renormalization Group equations
• Top mass from asymptotic safety
• Hilbert series and operator bases with derivatives in effective field theories
• Asymptotic safety: a simple example
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Viability of quantum-gravity induced ultraviolet completions for matter
• Higher order quark-mesonic scattering processes and the phase structure of QCD
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Mass difference for charged quarks from asymptotically safe quantum gravity
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Bootstrapping 3D Fermions with Global Symmetries
• Solutions of renormalization group flow equations with full momentum dependence
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Large N and the renormalization group
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Four loop renormalization of the Gross-Neveu model
• Critical exponents of O(N) models in fractional dimensions
• Computation of $\beta (g_c)$ at O(1/N^2) in the O(N) Gross Neveu Model in Arbitrary Dimensions
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Ising and Gross-Neveu model in next-to-leading order
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• $d=4$ as the critical dimensionality of asymptotically safe interactions
• Solving functional flow equations with pseudo-spectral methods
• Multi-meson Yukawa interactions at criticality
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Global flow of the Higgs potential in a Yukawa model
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Global Wilson-Fisher fixed points
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• Fixed points and the spontaneous breaking of scale invariance
• Critical $O(N)$ models in the complex field plane
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Scaling and superscaling solutions from the functional renormalization group
• Deconfined criticality from the QED${}_3$-Gross-Neveu model at three loops
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Lessons from conformally reduced quantum gravity
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• Momentum dependence of quantum critical Dirac systems
• Scaling solutions in the derivative expansion
• Universal behavior of coupled order parameters below three dimensions
• Operator product expansion coefficients in the exact renormalization group formalism
• Existence and Construction of Exact FRG Flows of a UV-Interacting Scalar Field Theory
• Multicritical points of the O(N) scalar theory in $2<d<4$ for large N

Cited by in corpus (6)

• QCD at finite temperature and density within the fRG approach: An overview
• Shocks and quark-meson scatterings at large density
• Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram
• Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data
• Universal and non-universal large deviations in critical systems
• Exact effective action for the O(N) vector model in the large N limit