Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model

Abstract

We discuss the analytic properties of the Callan-Symanzik beta-function beta(g) associated with the zero-momentum four-point coupling g in the two-dimensional phi^4 model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behavior of beta(g) at the fixed point g^*. We argue that beta'(g) = beta'(g^*) + O(|g-g^*|^{1/7}) for N=1 and beta'(g) = beta'(g^*) + O(1/\log |g-g^*|) for N > 2. Our claim is supported by an explicit calculation in the Ising lattice model and by a 1/N calculation for the two-dimensional phi^4 theory. We discuss how these nonanalytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.

arXiv comment18 pages. Discussion on Logarithmic CFT added in Appendix A. References updated. A note on the interpretation of the p_5 constant added. Final version, accepted for publication in Journal of Physics A

References in corpus (31)

• Critical Exponents of the N-vector model
• Logarithmic Operators in Conformal Field Theory
• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• A Local Logarithmic Conformal Field Theory
• On Modular Invariant Partition Functions of Conformal Field Theories with Logarithmic Operators
• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• High precision Monte Carlo study of the 3D XY-universality class
• On Fusion Rules in Logarithmic Conformal Field Theories
• A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy
• Singular Vectors in Logarithmic Conformal Field Theories
• Four-point renormalized coupling constant in O(N) models
• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
• Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination
• Critical amplitudes and mass spectrum of the 2D Ising model in a magnetic field
• Lattice Perturbation Theory for $O(N)$-Symmetric $\sigma$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory
• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• The effective potential of N-vector models: a field-theoretic study to O(ε^3)
• High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion
• The critical equation of state of three-dimensional XY systems
• Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets
• High-precision estimate of g4 in the 2D Ising model
• Field-Theoretic Techniques in the Study of Critical Phenomena
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Critical limit and anisotropy in the two-point correlation function of three-dimensional O(N) models
• Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional Φ^{4} field models
• Non-analyticity of the Callan-Symanzik beta-function of O(N) models
• Decoupling or nondecoupling: is that the $R_b$ question?
• Critical behavior of the correlation function of three-dimensional O(N) models in the symmetric phase

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