Critical behaviour of a O(n)-symmetric model with an antisymmetric tensor order parameter: the real-space renormalization group

Abstract

Critical behavior of the O(n)-symmetric model with antisymmetric tensor order parameter is studied by means of the renormalization group approach in the space of a fixed dimension. Previously this model was studied by the authors in collaboration with N. V.Antonov by means of ε-expansion. Within the framework of this approach, it was shown that non-trivial fixed points are present in the model only in the case n = 4, however, their infrared stability properties appeared to be sensitive to the accounting of the higher orders of perturbation theory and the asymptotic nature of ε-expansions. As a result, it was concluded that in order to obtain a reliable picture of critical behavior, besides accounting for the higher orders of perturbation theory, it is also necessary to explore the dependence of the results on the choice of a specific renormalization scheme. For this purpose in the present paper RG-functions and critical exponents of the model are calculated in form of pseudo-ε-expansions with a three-loop accuracy. The results obtained are in qualitative agreement with results of the Borel resummation of corresponding ε-expansions in three-loop approximation. Nevertheless, the numerical values of the critical exponents obtained by direct summation of the pseudo-ε-expansions and by the Borel resummation of the corresponding ε-expansions can differ quite significantly. Refs 33. Tables 6.