Magnetic suspectibility of the O(N) σ-model from high temperature expansions and scaling

High temperature expansions at 14th order and asymptotic scaling are used to reconstruct at any coupling the magnetic susceptibility of the non-linear O(N) σ-model. The method we use, a Pade resummation in a mapped variable, is shown to be exact in the N=∞ case. The results, which are in agreement with Monte Carlo data, show how the onset of scaling changes between O(4) and O(3), in a way compatible with the renormalization group asymptotic value. (orig.)