  We study the conditions under which the critical behavior of the
three-dimensional $mn$-vector model does not belong to the spherically
symmetrical universality class. In the calculations we rely on the
field-theoretical renormalization group approach in different regularization
schemes adjusted by resummation and extended analysis of the series for
renormalization-group functions which are known for the model in high orders of
perturbation theory. The phase diagram of the three-dimensional $mn$-vector
model is built marking out domains in the $mn$-plane where the model belongs to
a given universality class.
