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Компьютерное моделирование фазовых переходов в модели Изинга с дальними корреляциями

А.А. Бирюков, И. В. Дегтярева, Марк Александрович Шлеенков

Published Jan 1, 2012• 0 citations
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Abstract

In this article phase transitions in the modified two-dimensional Ising model with long-range correlations investigated. This model was studied with Monte-Carlo method and Metropolis algorithm. Critical temperature increase is shown in such model.

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AbstractPhase transitions and thermodynamic properties have been studied in the two-dimensional antiferromagnetic Ising model on a Kagome lattice by the Monte Carlo method with consideration for both nearest- and next-nearest-neighbor interaction. Using the histogram data analysis method, it has been shown that the studied model is characterized by a second-order phase transition. The temperature dependence of thermodynamic parameters has been revealed to exhibit abnormal behavior.

Physics of the Solid State•Jan 1, 2018•0 citations
The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.
The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.
The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q = 3 on square and hexagonal lattices. Considered systems with linear dimensions L × L = N, L = 21 ÷ 102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values ​​of the critical points of the Potts model on different lattices.
The influence of the external magnetic field on the phase transitions, thermodynamic and magnetic properties of the three-dimensional Ising model of antiferromagnetic on a body-centered cubic lattice taking into account the interactions of the second nearest neighbors is studied by the replica algorithm of the Monte Carlo method. A phase diagram of the dependence of the critical temperature on the external magnetic field has been constructed. It is shown that a second-order phase transition is observed in the considered range of magnetic field values