  We solve the spin-1 quantum Ising model with single-ion anisotropy by mapping
it onto a series of segmented spin-1/2 transverse Ising chains, separated by
the $S^z =0$ states called holes. A recursion formula is derived for the
partition function to simplify the summation of hole configurations. This
allows the thermodynamic quantities of this model to be rigorously determined
in the thermodynamic limit. The low temperature behavior is governed by the
interplay between the hole excitations and the fermionic excitations within
each spin-1/2 Ising segment. The quantum critical fluctuations around the Ising
critical point of the transverse Ising model are strongly suppressed by the
hole excitations.
