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In the model of finite number (up to 24) of point Ising-like magnetic dipoles with magnetostatic interaction on square 2D lattice within the framework of statistical physics, with using Gibbs formalism and by the means of Metropolis algorithm the heating dependence of temperature has been evaluated. The temperature dependence of the heat capacity on finite number of point dipoles has the finite value of maximum. Together with increase of the system in size the heating peak grows and moves to the area with higher temperature. The obtained results are useful in experimental verification of statistical models, as well as in development and testing of approximate calculation methods of systems with great number of particles.

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We present the simulation results of magnetic 2D and 3D structures with direct (for both of them) and Dzyaloshinskii-Moriya (DMI) (for 2D lattice) interactions in the frame of the Heisenberg model. We have adapted the multipath Metropolis algorithm for systems with complex types of exchange interactions and rough energy landscapes. We show the temperature behavior of magnetization, energy, and heat capacity, and reveal its critical temperatures and order parameter.

The critical phenomena on cobalt monolayer films were studied by means of computersimulation. Proposed approach on the base of data of scanning tunneling microscopy gives possibilityestimate of critical concentration needed for concentration transition into ferromagnetic state. Assumptionabout presence of critical switching field allowed simulated hysteresis loops for given 1.5,2.0, 2.5 and 3.0 ML cobalt samples in frame of Ising model, which ones have qualitative agreementwith magnetometric data.

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