COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL
Abstract. Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange interactions between the nearest J1 and second J2 neighbours. The main goal of the compute...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
Dagestan State Technical University
2017-07-01
|
| Series: | Вестник Дагестанского государственного технического университета: Технические науки |
| Subjects: | |
| Online Access: | https://vestnik.dgtu.ru/jour/article/view/368 |
| _version_ | 1797694964759527424 |
|---|---|
| author | Yarash K. Abuev Albert B. Babaev Pharkhat E. Esetov |
| author_facet | Yarash K. Abuev Albert B. Babaev Pharkhat E. Esetov |
| author_sort | Yarash K. Abuev |
| collection | DOAJ |
| description | Abstract. Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange interactions between the nearest J1 and second J2 neighbours. The main goal of the computer simulation was to elucidate the effects of ground state and areas of frustration on the thermodynamic and magnetic properties of antiferromagnetic structures described by the lowdimensional Potts model. Method The computer simulation is based on the Monte Carlo method. This method is implemented using the Metropolis algorithm in combination with the Wolff claster algorithm. The computer simulation was carried out for low-dimensional systems with periodic boundary conditions and linear dimensions L = 24124. Results On the basis of heat capacity and entropy analysis, phase transitions were observed in the considered model to possess exchange interaction parameters J1 <0 and J2 <0 in the variation intervals 0r<0.2 and 1.0<r2.0 (r=J2/J1). In the intermediate interval 0,2r1,0 there is no phase transition, and frustrations are observed. The temperature dependences of thermodynamic parameters, such as heat capacity, susceptibility and entropy, were obtained for all considered systems with linear dimensions L. The behaviour of these parameters, both at low and high temperatures, is discussed. The temperatures of the phase transitions are determined using the Binder fourth-order cumulant method. Conclusion Cases are shown in which, depending on the r-value, either a phase transition or a frustration is observed in the simulated system. It is proved that the competition between the exchange parameters of the first and second nearest neighbors in the r variation interval 0,2r1,0 leads to a degeneracy in the examined structure ground state; frustrations are additionally observed in the interval under consideration. On the basis of the obtained data, a phase diagram is constructed depending on the phase transition temperature and r-ratio. |
| first_indexed | 2024-03-12T03:04:29Z |
| format | Article |
| id | doaj.art-c78d9a991cf344648d41956aa26513ef |
| institution | Directory Open Access Journal |
| issn | 2073-6185 2542-095X |
| language | Russian |
| last_indexed | 2024-03-12T03:04:29Z |
| publishDate | 2017-07-01 |
| publisher | Dagestan State Technical University |
| record_format | Article |
| series | Вестник Дагестанского государственного технического университета: Технические науки |
| spelling | doaj.art-c78d9a991cf344648d41956aa26513ef2023-09-03T14:33:09ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2017-07-01441616910.21822/2073-6185-2017-44-1-61-69328COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODELYarash K. Abuev0Albert B. Babaev1Pharkhat E. Esetov2Институт физики им. Х.И. Амирханова Дагестанского научного центра РАНДагестанский государственный педагогический университетДагестанский государственный педагогический университетAbstract. Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange interactions between the nearest J1 and second J2 neighbours. The main goal of the computer simulation was to elucidate the effects of ground state and areas of frustration on the thermodynamic and magnetic properties of antiferromagnetic structures described by the lowdimensional Potts model. Method The computer simulation is based on the Monte Carlo method. This method is implemented using the Metropolis algorithm in combination with the Wolff claster algorithm. The computer simulation was carried out for low-dimensional systems with periodic boundary conditions and linear dimensions L = 24124. Results On the basis of heat capacity and entropy analysis, phase transitions were observed in the considered model to possess exchange interaction parameters J1 <0 and J2 <0 in the variation intervals 0r<0.2 and 1.0<r2.0 (r=J2/J1). In the intermediate interval 0,2r1,0 there is no phase transition, and frustrations are observed. The temperature dependences of thermodynamic parameters, such as heat capacity, susceptibility and entropy, were obtained for all considered systems with linear dimensions L. The behaviour of these parameters, both at low and high temperatures, is discussed. The temperatures of the phase transitions are determined using the Binder fourth-order cumulant method. Conclusion Cases are shown in which, depending on the r-value, either a phase transition or a frustration is observed in the simulated system. It is proved that the competition between the exchange parameters of the first and second nearest neighbors in the r variation interval 0,2r1,0 leads to a degeneracy in the examined structure ground state; frustrations are additionally observed in the interval under consideration. On the basis of the obtained data, a phase diagram is constructed depending on the phase transition temperature and r-ratio.https://vestnik.dgtu.ru/jour/article/view/368фрустрациифазовые переходымодель поттсатреугольная решетка |
| spellingShingle | Yarash K. Abuev Albert B. Babaev Pharkhat E. Esetov COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL Вестник Дагестанского государственного технического университета: Технические науки фрустрации фазовые переходы модель поттса треугольная решетка |
| title | COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL |
| title_full | COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL |
| title_fullStr | COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL |
| title_full_unstemmed | COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL |
| title_short | COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL |
| title_sort | computer simulation of antiferromagnetic structures described by the three vertex antiferromagnetic potts model |
| topic | фрустрации фазовые переходы модель поттса треугольная решетка |
| url | https://vestnik.dgtu.ru/jour/article/view/368 |
| work_keys_str_mv | AT yarashkabuev computersimulationofantiferromagneticstructuresdescribedbythethreevertexantiferromagneticpottsmodel AT albertbbabaev computersimulationofantiferromagneticstructuresdescribedbythethreevertexantiferromagneticpottsmodel AT pharkhateesetov computersimulationofantiferromagneticstructuresdescribedbythethreevertexantiferromagneticpottsmodel |