Critical behaviour of a O(n)-symmetric model with antisymmetric tensor order parameter: Four-loop approximation

Abstract

The critical behavior of the O(n)-symmetric φ4 model with an antisymmetric tensor order parameter is studied by means of the renormalization group approach. Previously, this model was studied in the framework of the three-loop approximation by means of ε-expansion with conformal Borel resummation technique and pseudo-ε-expansion. It was shown that the results of these approaches are in qualitative agreement with each other, however, the numerical values of the critical indices can differ quite significantly. Moreover, the question of the sensitivity of even qualitative results to the accounting of the higher orders of perturbation theory remained open. In the present paper, the RG functions and critical indices of the model are calculated up to four-loop accuracy within both approaches. Their analysis shows that the results of applying different approaches are qualitatively consistent both with each other and with the results of the three-loop analysis.