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.

PHASE TRANSITIONS OF THE MIXED-SPIN ISING MODEL ON A DECORATED LATTICE WITH THE NEAREST-NEIGHBOR INTERACTION BETWEEN DECORATING SPINS

2009 ◽  
Vol 23 (24) ◽  
pp. 4963-4976 ◽  
Author(s):  
A. BENYOUSSEF ◽  
A. EL KENZ ◽  
M. EL YADARI ◽  
M. LOULIDI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nearest Neighbors ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Neighbor Interaction ◽  
Mixed Spin

A mean-field approximation is developed for a decorated ferrimagnetic Ising model, in which the two magnetic atoms A and B have spins σ=1/2 and S=1, respectively. In this system, the exchange interaction between nearest-neighbors of atom B is taken into account. Some interesting phenomena, such as the appearance of three types of phase diagrams and the existence of one and two compensation points are found. Phase diagrams and temperature dependence of the magnetizations of the system are investigated in detail.

Magnetic Properties of the Random Mixture of the Classical Heisenberg Spins

1975 ◽  
Vol 53 (9) ◽  
pp. 854-860 ◽  
Author(s):  
Shigetoshi Katsura
Keyword(s):  
Critical Temperature ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Three Dimensional ◽  
Bethe Lattice ◽  
Zero Field ◽  
Qualitative Properties ◽  
Neighbor Interaction ◽  
Random Mixture ◽  
Ising Spins

The specific heat, the susceptibility, and the correlation function at zero field above the critical temperature of the random mixture (quenched site and bond problems) of the classical Heisenberg spins with nearest neighbor interaction were obtained exactly for the linear chain and for an infinite Bethe lattice (Bethe approximation of the two and three dimensional lattices) above the critical temperature. The results are simply expressed by the replacements of 2 cosh K → 4π (sinh K)/K and tanh K → L(K) (L(K) = Langevin function) for K = KAA, KAB, KBA, and KBB in the corresponding expressions of the random mixture of the Ising spins, and qualitative properties of both models are similar.

scholarly journals Frustrations and phase transitions in magnets of various dimensionality

2018 ◽  
Vol 185 ◽  
pp. 11002
Author(s):  
Felix Kassan-Ogly ◽  
Alexey Proshkin
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
External Magnetic Field ◽  
Specific Heat ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Exchange Interactions ◽  
Specific Model ◽  
Main Challenge ◽  
Transition Points

We studied magnetic orderings, phase transitions, and frustrations in the Ising, 3-state Potts and standard 4-state Potts models on 1D, 2D, and 3D lattices: linear chain, square, triangular, kagome, honeycomb, and body-centered cubic. The main challenge was to find out the causes of frustrations phenomena and those features that distinguish frustrated system from not frustrated ones. The spins may interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or higher-neighbor exchange interactions and via an external magnetic field that may be either competing or not. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is depend on the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the specific model and the lattice topology.

scholarly journals Влияние магнитного поля на термодинамические и магнитные свойства антиферромагнитной модели Изинга на объемно-центрированной кубической решетке

2020 ◽  
Vol 62 (2) ◽  
pp. 229
Author(s):  
А.К. Муртазаев ◽  
М.К. Рамазанов ◽  
К.Ш. Муртазаев ◽  
М.А. Магомедов ◽  
М.К. Бадиев
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
External Magnetic Field ◽  
Three Dimensional ◽  
Nearest Neighbors ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
The Monte Carlo Method ◽  
Body Centered Cubic Lattice ◽  
Second Order Phase Transition

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

scholarly journals Исследование термодинамических свойств модели Изинга на объемно-центрированной кубической решетке с конкурирующими обменными взаимодействиями

2018 ◽  
Vol 60 (9) ◽  
pp. 1798
Author(s):  
А.К. Муртазаев ◽  
М.К. Рамазанов ◽  
М.А. Магомедов ◽  
Д.Р. Курбанова
Keyword(s):  
Phase Transition ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Body Centered Cubic ◽  
Magnetic Structures ◽  
Cubic Lattice ◽  
The Monte Carlo Method ◽  
Antiferromagnetic Ising Model ◽  
Body Centered Cubic Lattice

AbstractUsing the Monte Carlo method, magnetic structures of the ground state and thermodynamic properties of the antiferromagnetic Ising model on a body-centered cubic lattice with competing exchange interactions are studied. The investigations are carried out for the ratio of the exchange interactions of next and nearest neighbors r = J _2/ J _1 = 2/3. All possible magnetic structures of the ground state for this ratio of exchange interactions have been obtained. It has been shown that at r = 2/3 the competition of exchange interactions does not lead to the appearance of frustration and degeneracy of the ground state. Based on the histogram data analysis, it has been shown that the phase transition of the second kind is observed in the model under study at r = 2/3.

scholarly journals Исследование фазовых переходов и термодинамических свойств модели Поттса с C-=SUB=-q-=/SUB=-=4 на гексагональной решетке с взаимодействиями вторых ближайших соседей

2020 ◽  
Vol 62 (3) ◽  
pp. 442
Author(s):  
М.К. Рамазанов ◽  
А.К. Муртазаев ◽  
М.А. Магомедов ◽  
М.К. Мазагаева
Keyword(s):  
Phase Transitions ◽  
Hexagonal Lattice ◽  
Magnetic Ordering ◽  
Nearest Neighbors ◽  
Magnetic Structures ◽  
First Order ◽  
The Monte Carlo Method ◽  
Cumulant Method ◽  
First Order Transition ◽  
Fourth Order Cumulant

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.

Phase Transition in Frustrated Heisenberg Antiferromagnet on a Triangular Lattice with Next-Nearest Neighbor Interactions

2012 ◽  
Vol 190 ◽  
pp. 417-420
Author(s):  
A.K. Murtazaev ◽  
M.K. Ramazanov ◽  
M.K. Badiev
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Heisenberg Model ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Finite Size ◽  
Replica Exchange ◽  
Heisenberg Antiferromagnet ◽  
Finite Size Scaling ◽  
The Monte Carlo Method

We study the critical behavior of three-dimensional antiferromagnet Heisenberg model with nearest-neighbor (J) and next-nearest-neighbor (J1) interactions by the Monte Carlo method using a high-effective replica exchange algorithm. Here is calculated a full set of main static critical exponents for values R =J1/J= 0.0; 0.025; 0.05; 0.075; 0.1; 0.115 using the finite-size scaling theory. A phase diagram of dependency of the critical temperature on a relation between nearest-neighbor and next-nearest-neighbor R is plotted.

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