Stability of the conventional fixed point of the nonlinear sigma-model in (2 + ε)-dimensions

The stability of the conventional fixed point of the nonlinear σ-model in (2 + ε)-dimensions has been studied by calculating the anomalous dimensions of leading order O(n - 1) symmetric gradient operators. The full dimensions, i.e. the canonical dimensions plus the anomalous dimensions, of these operators at the fixed point are found to be negative and therefore the fixed point is stable against the perturbation of these operators. The results indicate that as far as the O(n) symmetry-breaking regime is concerned, the conventional treatment of this model is adequate.