The parallel-tempering method has been applied to numerically study the thermodynamic behavior of a three-dimensional disordered antiferromagnetic Ising model with random fields at spin concentrations corresponding to regions of both weak and strong structural disorder. An analysis of the low-temperature behavior of the model convincingly shows that in the case of a weakly disordered samples there is realized an antiferromagnetic ordered state, while in the region of strong structural disorder the effects of random magnetic fields lead to the realization of a new phase state of the system with a complex domain structure consisting of antiferromagnetic and ferromagnetic domains separated by regions of a spin-glass phase and characterized by a spinglass ground state.
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