Global Wilson-Fisher fixed points

Abstract

The Wilson-Fisher fixed point with $O(N)$ universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed point solutions to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantitites such as scaling exponents and mass ratios are computed, for all $N$, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-$N$ results do not converge pointwise towards the exact infinite-$N$ limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.

28 pages, 10 figures, v2: explanations and refs added, to appear (NPB)

References in corpus (19)

• Exact evolution equation for the effective potential
• The critical exponents of the superfluid transition in He4
• Asymptotic safety in the f(R) approximation
• Ising exponents from the functional renormalisation group
• The local potential approximation in quantum gravity
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• The Higgs Mass and the Scale of New Physics
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Critical exponents of O(N) models in fractional dimensions
• High-accuracy scaling exponents in the local potential approximation
• Lee-Yang model from the functional renormalization group
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings
• Critical $O(N)$ models in the complex field plane
• Are there scaling solutions in the O(N)-models for large N in d>4?
• Convexity of the effective action from functional flows
• Towards Functional Flows for Hierarchical Models
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
• The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach

Cited by in corpus (23)

• The nonperturbative functional renormalization group and its applications
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Monte Carlo study of an improved clock model in three dimensions
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Lorentz invariance violations in the interplay of quantum gravity with matter
• Universal location of the Yang-Lee edge singularity in O(N) theories
• UV conformal window for asymptotic safety
• Essential renormalisation group
• Fixed points and the spontaneous breaking of scale invariance
• Asymptotic safety of scalar field theories
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Activating critical exponent spectra with a slow drive
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Functional flows for complex effective actions
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• The background field method and critical vector models
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Properties of the $\epsilon$-Expansion, Lagrange Inversion and Associahedra and the $O(1)$ Model
• Fermion Mass Generation without Symmetry Breaking
• Renormalization Flow of Nonlinear Electrodynamics
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• Critical and multicritical Lee-Yang fixed points in the local potential approximation