Non-analyticity of the Callan-Symanzik β-function of O(N) models.

In the framework of the 1/N expansion we show that the Callan-Symanzik beta-function associated with the four-point coupling g is non-analytic at its zero, i.e. at the fixed-point value g* of g. This singular behavior can be interpreted by renormalization group arguments, and written in terms of scaling correction exponents. We obtain accurate determinations of g* in 3-d and 2-d by exploiting two alternative approaches: the epsilon-expansion in the phi(4) formulation of the O(N) model, and the high-temperature expansion of the lattice N-vector (O(N) nonlinear sigma) model. These results are compared with the available estimates by other approaches, such as the fixed-dimension perturbative expansion, Monte Carlo simulations, etc... We also present results for the n-point renormalized coupling constants that parameterize the behavior of the effective potential in the high- and low-temperature phases.