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The Monte Carlo method is used to study long-period modulated structures in an anisotropic Ising model with competing interactions (ANNNI model). The character, particularities, and dependence of the modulated structures on the temperature and ratio of the exchange interaction constants between the nearest and next-to-nearest neighbors are determined. The phase diagram is constructed.

Models describing the critical properties of yttrium orthoferrite are proposed. The models are investigated by the Monte Carlo method. The main static critical exponents for the models are calculated using the formalism of the theory of finite-size scaling, and their universality classes are determined. The results can account for the contradiction between the experimentally observed and theoretically predicated pictures of the critical behavior of yttrium orthoferrite. It is shown that the models of YFeO3 are mainly described by the Ising universality class of critical behavior.

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