  On any torus $\mathbb{T}^d$, $d \geq 2$, we prove the existence of a
real-analytic diffeomorphism $T$ with a good approximation of type
$\left(h,h+1\right)$, a maximal spectral type disjoint with its convolutions
and a homogeneous spectrum of multiplicity two for the Cartesian square
$T\times T$. The proof is based on a real-analytic version of the Approximation
by Conjugation-method.
