  We study the multi-dimensional operator $(H_x
u)_n=\sum_{|m-n|=1}u_{m}+f(T^n(x))u_n$, where $T$ is the shift of the torus
$\T^d$. When $d=2$, we show the spectrum of $H_x$ is almost surely purely
continuous for a.e. $\alpha$ and generic continuous potentials. When $d\geq 3$,
the same result holds for frequencies under an explicit arithmetic criterion.
We also show that general multi-dimensional operators with measurable
potentials do not have eigenvalue for generic $\alpha$.
