Phase Transitions and Critical Properties of the Heisenberg Antiferromagnetic Model on a Body-Centered Cubic Lattice with Second Nearest Neighbor Interaction

2019 ◽  
Vol 129 (5) ◽  
pp. 903-910 ◽  
Author(s):  
A. K. Murtazaev ◽  
D. R. Kurbanova ◽  
M. K. Ramazanov
Keyword(s):  
Phase Transitions ◽  
Nearest Neighbor ◽  
Critical Properties ◽  
Body Centered Cubic ◽  
Neighbor Interaction ◽  
Cubic Lattice ◽  
Antiferromagnetic Model ◽  
Body Centered Cubic Lattice

Phase Transitions and the Critical Properties of the Heisenberg Model on a Body-Centered Cubic Lattice

2019 ◽  
Vol 61 (6) ◽  
pp. 1107-1112 ◽  
Author(s):  
A. K. Murtazaev ◽  
M. K. Ramazanov ◽  
D. R. Kurbanova ◽  
M. A. Magomedov ◽  
M. K. Badiev ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Heisenberg Model ◽  
Critical Properties ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Body Centered Cubic Lattice

Phase Transitions in Frustrated Ising Antiferromagnet on a Body-Centered Cubic Lattice with Next-Nearest Neighbor Interactions

2015 ◽  
Vol 233-234 ◽  
pp. 86-89
Author(s):  
Akay K. Murtazaev ◽  
Magomedsheykh K. Ramazanov ◽  
Djuma R. Kurbanova
Keyword(s):  
Phase Transitions ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Monte Carlo Algorithm ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Finite Dimensional ◽  
Ising Antiferromagnet ◽  
Antiferromagnetic Ising Model ◽  
Body Centered Cubic Lattice

The phase transitions in antiferromagnetic Ising model are studied on a body-centered cubic lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transitions of second order. A static magnetic critical indices is calculated using the finite-dimensional scaling theory.

scholarly journals Компьютерное моделирование фазовых переходов и критических свойств фрустрированной модели Гейзенберга на кубической решетке

2020 ◽  
Vol 62 (6) ◽  
pp. 868
Author(s):  
М.К. Рамазанов ◽  
А.К. Муртазаев
Keyword(s):  
Phase Transition ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Universality Class ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Cubic Lattice ◽  
Range Of Values ◽  
Antiferromagnetic Model ◽  
Second Order Phase Transition

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.

Computer simulation of phase transitions of the Heisenberg antiferromagnetic model

2019 ◽  
pp. 25-31
Author(s):  
M.K. Ramazanov ◽  
A.K. Murtazaev
Keyword(s):  
Computer Simulation ◽  
Phase Transitions ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Neighbor Interaction ◽  
A Value ◽  
The Monte Carlo Method ◽  
Antiferromagnetic Model

Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. The phase transitions of this model are studied. The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors $r = J_2 / J_1$ in the range $0.0 \leq r \leq 1.0$. The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.

scholarly journals Фазовые переходы в атиферромагнитной модели Гейзенберга на объемно-центрированной кубической решетке с учетом взаимодействий следующих ближайших соседей

2018 ◽  
Vol 60 (6) ◽  
pp. 1162
Author(s):  
А.К. Муртазаев ◽  
М.К. Рамазанов ◽  
Д.Р. Курбанова ◽  
М.К. Бадиев
Keyword(s):  
Nearest Neighbor ◽  
Three Dimensional ◽  
Monte Carlo Algorithm ◽  
Body Centered Cubic ◽  
Neighbor Interaction ◽  
First Order ◽  
First Order Phase Transition ◽  
Replica Exchange Monte Carlo ◽  
First Order Phase ◽  
Body Centered Cubic Lattice

AbstractBased on the replica exchange Monte Carlo algorithm and histogram analysis of data, the phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with allowance for the next-nearest-neighbor interaction are studied. The study is performed for the nextnearest- neighbor exchange interaction ratio of r = 1. It is established that, for this model, the transition from the antiferromagnetic to paramagnetic phase is a first-order phase transition.

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