  Vacancy defects in disordered magnetic materials are known to act as
effective spins, ``quasispins'', in response to an external magnetic field. In
the dilute limit, the contributions of such ``quasispins'' to the magnetic
susceptibility $\chi_\text{vac}(T)\propto N_\text{vac}/T$ are singular in the
limit of low temperatures $T$ and match those of free spins. With increasing
the density of vacancies, their interactions may become essential. Motivated by
frustrated and quasi-one-dimensional magnetic materials, we study analytically
quasispins and their interactions in a generic system that has short-range
antiferromagnetic order and lacks long-range order. We predict that if the
vacancy defect does not disrupt the short-range antiferromagnetic order around
it, the quasispin value matches the value of spins of the magnetic atoms in the
material, and the correlators of the quasispins of different vacancies match
the spin-spin correlators in the vacancy-free material. We confirm our
conclusions by exact calculations for Ising chains with nearest-neighbour and
next-to-nearest-neighbour interactions. We also compute the first virial
correction to the susceptibility of a magnetic material due to the interactions
of vacancy quasispins.
