Phase transitions in the four-component Potts model on a triangular lattice
- Authors: Babaev A.B.1, Murtazaev A.K.1
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Affiliations:
- Amirkhanov Institute of Physics Dagestan Federal Research Center, Russian Academy of Sciences
- Issue: Vol 125, No 7 (2024)
- Pages: 790-794
- Section: ЭЛЕКТРИЧЕСКИЕ И МАГНИТНЫЕ СВОЙСТВА
- URL: https://journals.rcsi.science/0015-3230/article/view/279657
- DOI: https://doi.org/10.31857/S0015323024070027
- EDN: https://elibrary.ru/JSCIEV
- ID: 279657
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Abstract
The Monte Carlo method is used to perform the simulation of four-component Potts model on a triangular lattice. Systems with linear dimensions of L × L = N and L = 10–160 are considered. Phase transitions in terms of the considered Potts model are studied using fourth-order Binder cumulants and histogram analysis of data. It is shown that, in the four-component Potts model on a triangular lattice, second-order transitions are observed.
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About the authors
A. B. Babaev
Amirkhanov Institute of Physics Dagestan Federal Research Center, Russian Academy of Sciences
Author for correspondence.
Email: b_albert78@mail.ru
Russian Federation, Makhachkala, 367030
A. K. Murtazaev
Amirkhanov Institute of Physics Dagestan Federal Research Center, Russian Academy of Sciences
Email: b_albert78@mail.ru
Russian Federation, Makhachkala, 367030
References
- Бэкстер Р. Точно решаемые модели в статистической механике / Пер. с англ. Е.П. Вольского, Л.И. Дайхина; Под ред. А.М. Бродского. М.: Мир, 1985. 486 с.
- Onsager L. Crystal statistics. 1: A two- dimensional model with an order-disorder transitions // Phys. Rev. 1944. V. 65. P. 117–149.
- Houtappel R.M.F. Order-disorder in hexagonal lattices // Physica. 1950. V. 16. P. 425.
- Kanô K., Naya S. Antiferromagnetism. The Kagome Ising Net // Prog. Theor. Phys. 1953. V. 10. P. 158.
- Wu F.Y. The Potts model // Rev. Mod. Phys. 1982. V. 54. № 1. P. 235–268.
- Wu F.Y. Exactly Solved Models: A Journey in Statistical Mechanics. London: World Scientific, 2009.
- Ермилов А.Н. Аналитический метод исследования стохастической модели Поттса // Физика элементарных частиц и атомного ядра. 1989. Т. 20. № 6. С. 1479.
- Wolff U. Collective Monte Carlo Updating for spin systems // Phys. Lett. 1989. V. 62. P. 361.
- Муртазаев А.К., Бабаев А.Б., Атаева Г.Я., Бабаев М.А. Фазовые переходы в разбавленной модели Поттса с числом состояний спина q=3 на квадратной решетке // ФТТ. 2022. Т. 64. С. 639.
- Муртазаев А.К., Бабаев А.Б. Вычислительная физика и проблемы фазовых переходов. М.: Физматлит, 2023. 184 с.
- Бабаев А.Б., Муртазаев А.К. Моделирование трехкомпонентной модели Поттса на гексагональной решетке методом Монте-Карло // ФММ. 2023. Т. 124. № 7. С. 577–583.
- Peczac P., Ferrenberg A.M., Landau D.P. High-accuracy Monte Carlo study of the three-dimensional classical Heisenberg ferromagnet // Phys. Rev. B. 1991. V. 43. P. 6087.
- Eichhorn K., Binder K. Monte Carlo investigation of the three-dimensional random-field three-state Potts model // J. Phys.: Condens. Matter. 1996. V. 8. Р. 5209.
- Loison D., Schotte K.D. First and second order transition in frustrated XY systems // Eur. Phys. J. B. 1998. V. 5. P. 735.
- Муртазаев А.К., Бабаев А.Б. Фазовые переходы в двумерных моделях Поттса на гексагональной решетке // Журнал экспериментальной и теоретической физики. 2022. Т. 161. № 6. С. 847–852.
- Фадеева М.А., Щур Л.Н. Моделирование четырехкомпонентной модели Поттса на гексагональной решетке методом Ванга–Ландау с контролируемой точностью // Журнал экспериментальной и теоретич. физики. 2022. Т. 162. С. 909–916.
Supplementary files
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Fig. 1. Four-component Potts model on a triangular lattice (a); description of adsorption based on the Potts model (b).
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Fig. 2. Dependence of the specific energy E on temperature for the four-component Potts model on a triangular lattice.
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Fig. 3. Dependence of specific heat capacity C on temperature for the four-component Potts model on a triangular lattice.
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Fig. 4. Dependence of the specific magnetic susceptibility χ on temperature for the four-component Potts model on a triangular lattice.
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Fig. 5. Dependence of spontaneous magnetization m on temperature for the four-component Potts model on a triangular lattice.
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Fig. 6. Dependence of Binder cumulants UL(T) on temperature for the four-component Potts model on a triangular lattice.
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Fig. 7. Dependence of Binder cumulants VL(T) on temperature for the four-component Potts model on a triangular lattice.
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Fig. 8. Histogram of energy distribution for the four-component Potts model on a triangular lattice.
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