On the stability of the O(N)-invariant and the cubic-invariant three-dimensional N-component renormalization-group fixed points in the hierarchical approximation
K. Pinn et al., On the stability of the O(N)-invariant and the cubic-invariant three-dimensional N-component renormalization-group fixed points in the hierarchical approximation, J STAT PHYS, 95(1-2), 1999, pp. 1-22
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.