The Renormalization Group and Two Dimensional Multicritical Effective Scalar Field Theory

Abstract

Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate non-perturbative methods. We apply a derivative expansion of the exact RG (Renormalization Group) equations in a form which allows the corresponding FP equations to appear as non-linear eigenvalue equations for the anomalous scaling dimension $\eta$. At zeroth order, only continuum limits based on critical sine-Gordon models, are accessible. At second order in derivatives, we perform a general search over all $\eta \ge .02$, finding the expected first ten FPs, and {\sl only} these. For each of these we verify the correct relevant qualitative behaviour, and compute critical exponents, and the dimensions of up to the first ten lowest dimension operators. Depending on the quantity, our lowest order approximate description agrees with CFT (Conformal Field Theory) with an accuracy between 0.2\% and 33\%; this requires however that certain irrelevant operators that are total derivatives in the CFT are associated with ones that are not total derivatives in the scalar field theory.

Note added on "shadow operators". Version to be published in Phys. Lett. B

References in corpus (3)

• The Exact Renormalisation Group and Approximate Solutions
• Derivative Expansion of the Exact Renormalization Group
• On Truncations of the Exact Renormalization Group

Cited by in corpus (64)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Nonperturbative Evolution Equation for Quantum Gravity
• The nonperturbative functional renormalization group and its applications
• Exact Renormalization Group Equations. An Introductory Review
• An Introduction to the Nonperturbative Renormalization Group
• Fundamentals of the Exact Renormalization Group
• Lectures on the functional renormalization group method
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Asymptotic safety in the f(R) approximation
• Phase Diagram of Superconductors from Non-Perturbative Flow Equations
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Three dimensional massive scalar field theory and the derivative expansion of the renormalization group
• Effective average action in statistical physics and quantum field theory
• Background independence in a background dependent renormalization group
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Background independent exact renormalization group for conformally reduced gravity
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Multi-meson Yukawa interactions at criticality
• Asymptotic solutions in asymptotic safety
• Multicritical behavior in models with two competing order parameters
• Momentum Scale Expansion of Sharp Cutoff Flow Equations
• Scaling Solutions in Continuous Dimension
• Lee-Yang model from the functional renormalization group
• Critical Phenomena in Continuous Dimension
• Fixed point structure of the conformal factor field in quantum gravity
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Quantum Liouville Field Theory as Solution of a Flow Equation
• Non-Compact Pure Gauge QED in 3D is Free
• Phase Diagram and Fixed-Point Structure of two dimensional N=1 Wess-Zumino Models
• Properties of derivative expansion approximations to the renormalization group
• Comparison of renormalization group schemes for sine-Gordon type models
• A note on scaling arguments in the effective average action formalism
• Are there scaling solutions in the O(N)-models for large N in d>4?
• Supersymmetry breaking as a quantum phase transition
• C Function Representation of the Local Potential Approximation
• Functional Renormalization and $\overline{\text{MS}}$
• The fate of non-polynomial interactions in scalar field theory
• Exact renormalization group study of fermionic theories
• Isotropic Lifshitz point in the O(N) Theory
• Scaling solutions in the derivative expansion
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Universal behavior of coupled order parameters below three dimensions
• Provable properties of asymptotic safety in $f(R)$ approximation
• 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
• Exact Renormalization Group for O(4) Gauged Supergravity
• Conformal invariance and vector operators in the $O(N)$ model
• Scheme dependence of asymptotically free solutions
• Solutions of the Polchinski ERG equation in the O(N) scalar model
• Simulation of static critical phenomena in non-ideal fluids with the Lattice Boltzmann method
• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Non-perturbative scaling in the scalar theory
• Renormalization of multicritical scalar models in curved space
• Polchinski ERG Equation in O(N) Scalar Field Theory
• The Universal Equation of State near the Critical Point of QCD
• Spectral Renormalization Group for the Gaussian model and ${\psi }^4$ theory on non-spatial networks
• Exact renormalization group approach in scalar and fermionic theories
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Effective Field Theory with a Variable Ultraviolet Cutoff
• Functional truncations in asymptotic safety for quantum gravity
• One-dimensional long-range Ising model: two (almost) equivalent approximations