Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop RG expansions

Original · EN

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)-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: Ncᶜ =1/2 Ncʳ. The numerical value Ncᶜ=1.447 ± 0.020 is obtained from resumming the known five-loop -series for Ncʳ. Since Ncᶜ < 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: =1.404(25), ν=0.715(10), =0.0343(20) for N=2 and =1.390(25), ν=0.702(10), =0.0345(15) for N=3.