  We study a stability border of a region where nontrivial critical behaviour
of an $n$-vector model with long-range power-law decaying interactions is
induced by the presence of a structural disorder (e.g. weak quenched dilution).
This border is given by the marginal dimension of the order parameter $n_c$
dependent on space dimension, $d$, and a control parameter of the interaction
decay, $\sigma$, below which the model belongs to the new dilution-induced
universality class. Exploiting the Harris criterion and recent
field-theoretical renormalization group results for the pure model with
long-range interactions we get $n_c$ as a three loop
$\epsilon=2\sigma-d$-expansion. We provide numerical values for $n_c$ applying
series resummation methods. Our results show that not only the Ising systems
($n=1$) can belong to the new disorder-induced long-range universality class at
$d=2$ and $d=3$.
