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We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the "kagome-ice" problem. We discuss the similarity and dissimilarity of the magnetization curves of the "kagome-ice" state and the twodimensional kagome lattice.

We perform the high-performance computation of the ferromagnetic Ising model on the pyrochlore lattice. We determine the critical temperature accurately based on the finite-size scaling of the Binder ratio. Comparing with the data on the simple cubic lattice, we argue the universal finite-size scaling. We also calculate the classical XY model and the classical Heisenberg model on the pyrochlore lattice.

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We study the residual entropy of the nearest-neighbor spin-ice model in a magnetic field along the [111] direction using the Wang-Landau Monte Carlo method, with a special attention to dilution effects. For a diluted model, we observe a stepwise decrease of the residual entropy as a function of the magnetic field, which is consistent with the finding of the five magnetization plateaus in a previous replica-exchange Monte Carlo study by Peretyatko et al. [Phys. Rev. B 95, 144410 (2017)]. We find large peaks of the residual entropy due to the degeneracy at the crossover magnetic fields, hc/J = 0, 3, 6, 9, and 12, where h and J are the magnetic field and the exchange coupling, respectively. In addition, we also study the residual entropy of the diluted antiferromagnetic Ising models in a magnetic field on the kagome and triangular lattices. We again observe large peaks of the residual entropy, which are associated with multiple magnetization plateaus for the diluted model. Finally, we discuss the interplay of dilution and magnetic fields in terms of the residual entropy.

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We utilize the Metropolis algorithm to obtain statistical averages of the domain wall length in a FePt granular structure after remagnetization is performed by an ultrashort polarized laser impulse. We propose and check the cluster-size-based order parameter, which along with magnetization, shows the domain wall length, and as a consequence, the average cluster size in the system. We treat the inverse Faraday effect as an external directed magnetic field and show impulse time- and laser power- dependent estimates within the Heisenberg model.

Magnetic films, in which magnetic vortex textures - skyrmions appear because of competition between the direct Heisenberg exchange and the Dzyaloshinskii-Moriya interaction, were studied using the Monte-Carlo simulation technique. The conditions for the nucleation and stable existence of magnetic skyrmions in magnetic films in the frame of the classical Heisenberg model were considered in the paper. The process of nucleation of skyrmions with increasing of the external magnetic field was studied, various phases into which the Heisenberg spin system passes were recognized. A phase diagram was plotted: it shows the behavior of the system at the constant value of temperature depending on values of an external magnetic field and Dzyaloshinskii-Moriya interaction.