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 sca
ling correction exponents.
We obtain accurate determinations of g* in 3-d and 2-d by exploiting two al
ternative approaches: the epsilon-expansion in the phi(4) formulation of th
e 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 e
stimates by other approaches, such as the fixed-dimension perturbative expa
nsion, Monte Carlo simulations, etc...
We also present results for the n-point renormalized coupling constants tha
t parameterize the behavior of the effective potential in the high- and low
-temperature phases.