The critical behavior of a model describing phase transitions in 3D antiferromagnets with
2N-component real order parameters is studied within the renormalization-group (RG) approach. The RG functions are calculated in the three-loop order and resummed by the generalized Pad\'e-Borel procedure preserving the specific symmetry properties of the model. An anisotropic stable fixed point is found to exist in the RG flow diagram for
N> 2 and lies near the Bose fixed point; corresponding critical exponents are close to those of the
XY model. The accuracy of the results obtained is discussed and estimated.
The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferromagnets with 2N-component (N>1) real order parameters as well as the structural transition in NbO 2 crystal is studied within the field-theoretical renormalization-group (RG) approach in three and (4-∊)-dimensions. Perturbative expansions for RG functions are calculated up to three-loop order and resummed, in 3D, by means of the generalized Padé–Borel procedure which is shown to preserve the specific symmetry properties of the model. It is found that a stable fixed point does exist in the three-dimensional RG flow diagram for N>1, in accordance with predictions obtained earlier within the ∊-expansion. Fixed-point coordinates and critical-exponent values are presented for physically interesting cases N=2 and N=3. In both cases critical exponents are found to be numerically close to those of the 3DXY model. The analysis of the results given by the ∊-expansion and by the RG approach in three dimensions is performed resulting in a conclusion that the latter provides much more accurate numerical estimates.
The critical behavior of an MN-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 $(4-2\ve)$-dimensions. Using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced for generic M and N and resummed by the Borel transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases M=2 and N=2, N=3 shows that the model has a three-dimensionally stable fixed point different from the Bose one. The critical dimensionality is proved to be exactly two times smaller than its counterpart in the real cubic model: N_c^C ={1/2} N_c^R. The numerical value
NcC=1.447±0.020 is obtained from resumming the known five-loop $\ve$-series for N_c^R. Since N_c^C < 2, the critical thermodynamics of the model relevant to the phase transitions in real substances should be governed by the complex cubic fixed point with a new set of critical exponents: $\gm=1.404(25)$,
ν=0.715(10), $\et=0.0343(20)$ for N=2 and $\gm=1.390(25)$,
ν=0.702(10), $\et=0.0345(15)$ for N=3.