High-accuracy scaling exponents in the local potential approximation

Abstract

We test equivalences between different realisations of Wilson's renormalisation group by computing the leading, subleading, and anti-symmetric corrections-to-scaling exponents, and the full fixed point potential for the Ising universality class to leading order in a derivative expansion. We discuss our methods with a special emphasis on accuracy and reliability. We establish numerical equivalence of Wilson-Polchinski flows and optimised renormalisation group flows with an unprecedented accuracy in the scaling exponents. Our results are contrasted with high-accuracy findings from Dyson's hierarchical model, where a tiny but systematic difference in all scaling exponents is established. Further applications for our numerical methods are briefly indicated.

9 pages, 7 figures, comparison and discussion/conclusions sharpened, references added

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Cited by in corpus (42)

• Fundamentals of the Exact Renormalization Group
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Further evidence for asymptotic safety of quantum gravity
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Asymptotic safety: a simple example
• Ising exponents from the functional renormalisation group
• The QCD Phase Boundary from Quark-Gluon Dynamics
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Ising and Gross-Neveu model in next-to-leading order
• Critical behavior in spherical and hyperbolic spaces
• Solving functional flow equations with pseudo-spectral methods
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Functional renormalization for Bose-Einstein Condensation
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Global Wilson-Fisher fixed points
• Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings
• Critical $O(N)$ models in the complex field plane
• Asymptotic safety of scalar field theories
• Scaling functions for the O(4)-model in d=3 dimensions
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Finite-Size Scaling behavior in the O(4)-Model
• Brans-Dicke theory in the local potential approximation
• Functional renormalization group approach to the Yang-Lee edge singularity
• N=1 Wess Zumino Model in d=3 at zero and finite temperature
• 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
• Phases of supersymmetric O(N) theories
• The fate of non-polynomial interactions in scalar field theory
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Universal behavior of coupled order parameters below three dimensions
• Revisiting the local potential approximation of the exact renormalization group equation
• Towards Functional Flows for Hierarchical Models
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
• Stability of fixed points and generalized critical behavior in multifield models
• Conformal mappings versus other power series methods for solving ordinary differential equations: illustration on anharmonic oscillators
• The local potential approximation in the background field formalism
• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state
• Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice