  It is widely expected that the realization of scale invariance in the
critical regime implies conformal invariance for a large class of systems. This
is known to be true if there exist no integrated operator which transforms like
a vector under rotations and which has scaling dimension $-1$. In this article
we give exact expressions for the critical exponents of some of these vector
operators. In particular, we show that one operator has scaling dimension
exactly 3 in any space dimension. This operator turns out be the leading
operator at least in $d=2$ and $d=4$. Moreover, we prove that the operator
previously considered in Monte-Carlo simulations has also scaling dimension
exactly $3$ in any dimension.
