  Within the four-loop $\ve$ 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 $N_c^C={1/2} N_c^R$ established
for the real and complex hypercubic models.
