Nonanalyticity of the Callan-Symanzik β-function of two-dimensional O(N) models

We discuss the analytic properties of the Callan-Symanzik β-function β(g) associated with the zero-momentum four-point coupling g in the two-dimensional φ4 model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behavior of β(g) at the fixed point g∗. We find that β(g) is not analytic at g = g∗: in the Ising model, β(g) has an expansion for g → g∗ with noninteger power corrections; for N ≥ 3, negative powers of log |g∗ − g| appear. We discuss how these nonanalytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.