Critical behavior of certain antiferromagnets with complicated ordering: Four-loop $\ve$-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 $(4-\ve)$ 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 N=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 the complex and real hypercubic models.

LaTeX, 16 pages, no figures. Expands on cond-mat/0109338 and includes detailed formulas

References in corpus (3)

• Critical behavior of the three-dimensional XY universality class
• Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop εexpansion
• On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

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