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 ${\chi }_{\text{vac}}\left(T\right)\propto N_{\text{vac}}/T$ 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 show by exact computation that the correlation of the quasispins of different vacancies matches the spin-spin correlators in the vacancy-free materials for Ising chains with nearest-neighbor and next-to-nearest-neighbor interactions. We also compute the first virial correction to the susceptibility of a magnetic material due to the interactions of vacancy quasispins. We then provide a phenomenological generalization of our results to 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.

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• Classical statistical mechanics
• Magnetic interactions
• Magnetic susceptibility
• Magnetism
• 1-dimensional spin chains
• 1-dimensional systems
• Antiferromagnets
• Disordered systems
• Exact solutions for many-body systems
• Ising model
• Virial theorem