The stability of a cubic fixed point in three dimensions from the renormalization group

Abstract

The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the $\bt$-functions are calculated for arbitrary $N$. The critical dimensionality $N_c=2.89 \pm 0.02$ and the stability matrix eigenvalues estimates obtained on the basis of the generalized Pad$\acute{\rm e}$-Borel-Leroy resummation technique are shown to be in a good agreement with those found recently by exploiting the five-loop $\ve$-expansions.