On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Within the four-loop $\varepsilon$ expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality $N_c^C=1.445(20)$ obtained from six loops via the exact relation $N_c^C=\frac{1}{2} N_c^R$ established for the real and complex hypercubic models.