  We calculate a marginal order parameter dimension $m_c$ which in a weakly
diluted quenched $m$-vector model controls the crossover from a universality
class of a ``pure'' model ($m>m_c$) to a new universality class ($m<m_c$).
Exploiting the Harris criterion and the field-theoretical renormalization group
approach allows us to obtain $m_c$ as a five-loop $\epsilon$-expansion as well
as a six-loop pseudo-$\epsilon$ expansion. In order to estimate the numerical
value of $m_c$ we process the series by precisely adjusted Pad\'e--Borel--Leroy
resummation procedures. Our final result $m_c=1.912\pm0.004<2$ stems from the
longer and more reliable pseudo-$\epsilon$ expansion, suggesting that a weak
quenched disorder does not change the values of $xy$-model critical exponents
as it follows from the experiments on critical properties of ${\rm He}^4$ in
porous media.
