  The critical thermodynamics of an $MN$-component field model with cubic
anisotropy relevant to the phase transitions in certain crystals with
complicated ordering is studied within the four-loop $\ve$ expansion using the
minimal subtraction scheme. Investigation of the global structure of RG flows
for the physically significant cases M=2, N=2 and M=2, N=3 shows that the model
has an anisotropic stable fixed point with new critical exponents. The critical
dimensionality of the order parameter is proved to be equal to
$N_c^C=1.445(20)$, that is exactly half its counterpart in the real hypercubic
model.
