  Applying the (infinite) density-matrix renormalisation group technique, we
explore the effect of an explicit dimerisation on the ground-state phase
diagram of the spin-1 $XXZ$ chain with single-ion anisotropy $D$. We
demonstrate that the Haldane phase between large-$D$ and antiferromagnetic
phases survives up to a critical dimerisation only. As a further new
characteristic the dimerisation induces a direct continuous Ising quantum phase
transition between the large-$D$ and antiferromagnetic phases with central
charge $c=1/2$, which terminates at a critical end-point where $c=7/10$.
Calculating the critical exponents of the order parameter, neutral gap and
spin-spin-correlation function, we find $\beta=1/8$ (1/24), $\nu=1$ (5/9), and
$\eta=1/4$ (3/20), respectively, which proves the Ising (tricritical Ising)
universality class in accordance with field-theoretical predictions.
