  Critical behaviour of the O(n)-symmetric $\phi^{4}$-model with an
antisymmetric tensor order parameter is studied by means of the field-theoretic
renormalization group (RG) in the leading order of the
$\varepsilon=4-d$-expansion (one-loop approximation). For $n=2$ and 3 the model
is equivalent to the scalar and the O(3)-symmetric vector models, for $n\ge4$
it involves two independent interaction terms and two coupling constants. It is
shown that for $n>4$ the RG equations have no infrared (IR) attractive fixed
points and their solutions (RG flows) leave the stability region of the model.
This means that fluctuations of the order parameter change the nature of the
phase transition from the second-order type (suggested by the mean-field
theory) to the first-order one. For $n=4$, the IR attractive fixed point exists
and the IR behaviour is non-universal: if the coupling constants belong to the
basin of attraction for the IR point, the phase transition is of the second
order and the IR critical scaling regime realizes. The corresponding critical
exponents $\nu$ and $\eta$ are presented in the order $\varepsilon$ and
$\varepsilon^{2}$, respectively. Otherwise the RG flows pass outside the
stability region and the first-order transition takes place.
