Critical behavior of certain antiferromagnets with complicated ordering: Four-loop<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ɛ</mml:mi></mml:math>-expansion analysis

Abstract

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 $4\ensuremath{-}\ensuremath{\varepsilon}$ 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 ${N}_{c}=\frac{1}{2}{n}_{c}$ established for complex and real hypercubic models.