  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.
