  The low-temperature behavior of the static magnetic susceptibility $\chi(T)$
of exchange-disordered antiferromagnetic spin chains is investigated. It is
shown that for a relatively small and even number of spins in the chain, two
exchange distributions which are expected to occur in nanochains of P donors in
silicon lead to qualitatively distinct behaviors of the low-temperature
susceptibility. As a consequence, magnetic measurements might be useful to
characterize whether a given sample meets the requirements compatible with
Kane's original proposalfor the exchange gates in a silicon-based quantum
computer hardware. We also explore the dependence of $\chi(T)$ on the number of
spins in the chain as it increases towards the thermodynamic limit, where any
degree or distribution of disorder leads to the same low-temperature scaling
behavior. We identify a crossover regime where the two distributions of
disorder may not be clearly differentiated, but the characteristic scaling of
the thermodynamic limit has not yet been reached.
