Critical behavior of certain antiferromagnets with complicated ordering:: Four-loop ε-expansion analysis -: art. no. 214423

The critical behavior of a complex N-component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in 4-epsilon dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping, Investigation of the global structure of RG flows for the physically significant cases N = 2 and 3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality N-c = 1.445(20) obtained from six loops via the exact relation N-c = 1/2n(c) established for complex and real hypercubic models.