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

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

2000-05-26

arxiv.org/abs/hep-th/0005254v3

J.Phys.A33:8155-8170,2000

Physics

High Energy Physics

High Energy Physics - Theory

18 pages. Discussion on Logarithmic CFT added in Appendix A. References updated. A note on the interpretation of the p_5 const

Scientific paper

10.1088/0305-4470/33/46/301

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.

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