The magnetic susceptibility of exchange-disordered antiferromagnetic finite chains

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.