We present a first-principles study of the physical properties of the disordered Ni 2−x MnSb alloys which form a continuous series connecting two typical members of the Heusler alloy family: namely, the half-metallic semi-Heusler alloy NiMnSb ͑x =1͒ and related metallic Heusler alloy Ni 2 MnSb ͑x =0͒. Magnetic moments, exchange interactions, magnon spectra, and Curie temperatures at ambient and elevated pressures are determined and compared with available experimental data. The spin-spin

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... tion functions at the critical temperature are also calculated. The pair exchange interactions and corresponding classical Heisenberg Hamiltonian are derived from self-consistent electronic structure calculations using a magnetic force theorem. Heusler alloys NiMnSb and Ni 2 MnSb exhibit strikingly different asymptotic behavior of exchange interactions with the distance between magnetic atoms. The Curie temperatures are estimated using multisublattice versions of the mean-field approximation, random-phase approximation, and Monte Carlo simulations. The robustness of the results with respect to the effect of correlations beyond the local density approximation, the selected reference state used for mapping to the Heisenberg Hamiltonian, and the applied mapping procedure are also discussed.