THE STABILITY OF THE O(N) INVARIANT FIXED-POINT IN 3 DIMENSIONS

We study the stability of the O(N) fixed point in three dimensions und er perturbations of the cubic type. We address this problem in the thr ee cases N = 2, 3, 4 by using finite-size scaling techniques and high- precision Monte Carlo simulations. It is well known that there is a cr itical value: 2 < N-c < 4 below which the O(N) fixed point is stable a nd above which the cubic fixed point becomes the stable one. Whilst we cannot exclude that N-c < 3, as recently claimed, our analysis strong ly suggests that N-c coincides with 3.