On the stability of the O(N)-invariant and the cubic-invariant three-dimensional N-component renormalization-group fixed points in the hierarchical approximation

We compute renormalization-group fixed points and their spectrum in an ultr alocal approximation. Wt study a case of two competing nontrivial fixed poi nts for a three-dimensional real N-component field. the O(N)-invariant fixe d point vs. the cubic-invariant fixed point. We compute the critical value N-c of the cubic phi(4)-perturbation at the O(N)-fixed point. The O(N)-fixe d point is stable under a cubic phi(4)-perturbation below N-c; above N-c it is unstable. The Critical value comes out as 2.219435 < N-c < 2.219436 in thc ultralocal approximation. We also compute the critical value of N at th e cubic invariant fixed point. Within the accuracy of our computations. the two values coincide.