  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.
