On the Stability of the O(N)-Invariant and the Cubic-Invariant Three-Dimensional N-Component Renormalization-Group Fixed Points in the Hierarchical Approximation

摘要

We compute renormalization-group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing nontrivial fixed points for a three-dimensional real N-component field: the O(N)-invariant fixed 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)-fixed 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