Abstract:The phase transitions and critical phenomena of the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with next and next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. Investigations are carried out for relations of exchange interaction values of next and next-nearest neighbors in the range of k values [0.0, 0.6]. A behavior of phase transitions is analyzed by the histogram method. A whole set of main static critical exponents is estimated… Show more
“…В дальнейшем, гораздо позже, в работах [31][32][33][34][35] и других подобные немонотонные температурные зависимости были получены при исследовании теплоемкости в малых ограниченных системах l << L. Для примера на рис. 3. приведены немонотонные температурные зависимости теплоемкости в 4 Не в малых ограниченных системах в условиях невесомости космического полета.…”
Section: немонотонные температурные зависимости теплоемкости и воспри...unclassified
The fluctuation-dispersed structure of small limited systems in critical condition is proposed on the basis of macro-systems phase transitions fluctuation theory. A distinctive feature of this structure is the equality of the number of order parameter fluctuations Nf(s) in the surface layer s = 4πl2 with the thiсkness l and the number of order parameter fluctuations Nf(v) in volume v = 4/3⋅π(l−2Rc)3. Based on this equation the linear size of a small spherical system have been evaluated, the relationship between the thermodynamic parameters has been determined – the temperature and the chemical potential with the linear size of the system which are similar to relations of M. Fisher t~1−1/ν, μ~l−1/ξ. Based on the quality similarities of the non-monotonic temperature dependences of various properties of macroinhomogeneous systems in the Earth gravity field and the non-monotonic temperature dependences of small confined systems properties under critical condition the equation of state has been proposed for small confined systems. This equation has been tested on the basis of experimental data from various properties of small confined systems.
“…В дальнейшем, гораздо позже, в работах [31][32][33][34][35] и других подобные немонотонные температурные зависимости были получены при исследовании теплоемкости в малых ограниченных системах l << L. Для примера на рис. 3. приведены немонотонные температурные зависимости теплоемкости в 4 Не в малых ограниченных системах в условиях невесомости космического полета.…”
Section: немонотонные температурные зависимости теплоемкости и воспри...unclassified
The fluctuation-dispersed structure of small limited systems in critical condition is proposed on the basis of macro-systems phase transitions fluctuation theory. A distinctive feature of this structure is the equality of the number of order parameter fluctuations Nf(s) in the surface layer s = 4πl2 with the thiсkness l and the number of order parameter fluctuations Nf(v) in volume v = 4/3⋅π(l−2Rc)3. Based on this equation the linear size of a small spherical system have been evaluated, the relationship between the thermodynamic parameters has been determined – the temperature and the chemical potential with the linear size of the system which are similar to relations of M. Fisher t~1−1/ν, μ~l−1/ξ. Based on the quality similarities of the non-monotonic temperature dependences of various properties of macroinhomogeneous systems in the Earth gravity field and the non-monotonic temperature dependences of small confined systems properties under critical condition the equation of state has been proposed for small confined systems. This equation has been tested on the basis of experimental data from various properties of small confined systems.
Magnetic structures of the ground state, phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice with next-nearest neighbors interactions are investigated by the Monte Carlo method based on the Wang-Landau algorithm. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to the appearance of frustration and a violation of magnetic ordering. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.
“…Второй член характеризует антиферромагнитное взаимодействие вторых ближайших соседей, находящихся в том же слое (J 2 < 0). В настоящее время ФП и критические свойства фрустрированных спиновых систем на основе микроскопических гамильтонианов довольно успешно изучаются методами МК [12][13][14][15][16][17][18]. Методы МК позволяют исследовать физические свойства спиновых систем практически любой сложности.…”
The phase transitions and critical properties of the Heisenberg antiferromagnetic model on a cubic lattice with nearest and next-nearest-neighbor interactions are investigated by the replica Monte Carlo method. The range of values of the interaction of the next-nearest-neighbor is considered 0.0 ≤ r ≤ 1.0. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. The values of all the main static critical exponents are calculated by means of the finite-size scaling theory. It is shown that the universality class of the critical behavior of this model is preserved in the range of 0.0 ≤ r ≤ 0.4.
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