Critical behavior of certain antiferromagnets with complicated ordering: Four-loop $\ve$-expansion analysis

Details Critical behavior of certain antiferromagnets with complicated ordering: Four-loop $\ve$-expansion analysis Critical behavior of certain antiferromagnets with complicated ordering: Four-loop $\ve$-expansion analysis

2001-11-19

arxiv.org/abs/cond-mat/0111330v1

Phys. Rev. B 64, 214423 (2001) (9 pages)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevB.64.214423

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 $(4-\ve)$ 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 $N_c={1/2} n_c$ established for the complex and real hypercubic models.

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