Modeling of three-state antiferromagnetic potts model on a simple cubic lattice by the monte carlo method
- 作者: Babaev A.B.1, Murtazaev A.K.1
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隶属关系:
- Amirkhanov Institute of Physics of the Daghestan Federal Research Centre of the Russian Academy of Sciences
- 期: 卷 126, 编号 6 (2025)
- 页面: 674-679
- 栏目: ЭЛЕКТРИЧЕСКИЕ И МАГНИТНЫЕ СВОЙСТВА
- URL: https://bakhtiniada.ru/0015-3230/article/view/322663
- DOI: https://doi.org/10.31857/S0015323025060054
- ID: 322663
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详细
Computer simulation of phase transitions in a three-state antiferromagnetic Potts model on a simple cubic lattice is carried out. Using the Monte Carlo method, the temperature dependences of the order parameter mAF, the susceptibility χ, and the heat capacity C. Systems with linear dimensions L×L×L=N, L=10–50 are considered. Using histogram data analysis and the fourth-order Binder cumulant method it is shown that a second-order phase transition occurs in the Potts model under consideration. The critical temperature Tc has been determined with good accuracy.
作者简介
A. Babaev
Amirkhanov Institute of Physics of the Daghestan Federal Research Centre of the Russian Academy of Sciences
Email: b_albert78@mail.ru
Makhachkala, 367010 Russia
A. Murtazaev
Amirkhanov Institute of Physics of the Daghestan Federal Research Centre of the Russian Academy of Sciences
编辑信件的主要联系方式.
Email: b_albert78@mail.ru
Makhachkala, 367010 Russia
参考
- Мушников Н.В. Магнетизм и магнитные фазовые переходы. Екатеринбург: Урал. ун-т, 2017. 168 с.
- Стишов С.М., Петрова А.Е. Критические точки и фазовые переходы // ЖЭТФ. 2020. Т. 158. С. 1215–1224.
- Бекстер Р. Точно решаемые модели в статистической механике. М.: Мир, 1985. 488 с
- Wu F.Y. The Potts model // Rev. Mod. Phys. 1982. V. 54. P. 235.
- Wu F.Y. Exactly Solved Models: A Journey in Statistical Mechanics World Scientific. World Sci. Pub. Co Inc., 2009. 641 p.
- Loulidi M. Some analytical results on the bond diluted q-state Potts model // Physica A. 2000. V. 287. P. 177–184.
- Guttmann A.J., Enting I.G. Series studies of the Potts model: III. The 3-state model on the simple cubic lattice // J. Phys. A.: Math. Gen. 1994. V. 27. P. 5801–5812.
- Banavar J., Grest G.S., Jasnow D. Ordering and Phase Transitions in Antiferromagnetic Potts Models // Phys. Rev. Letters. 1980. V. 45. Р. 1424.
- Grest G.S., Banavar J. Monte Carlo Study of the Antiferromagnetic Potts Model in Two Dimensions // Physical Review Letters. 1981. V. 46. Р. 1458.
- Wang J.-S., Swendsen R.H., Kotecký R. Three-State Antiferromagnetic Potts Models: A Monte Carlo Study // Phys. Rev. B. 1990. V. 42. Р. 2465.
- Fisher M.E., Barber M.N. Scaling theory for finite-size effects in the critical region // Phys. Rev. Lett. 1972. V. 28. Nо. 23. P. 1516–1519.
- Gottlob A.P., Hasenbusch M. Three-State Anti-Ferromagnetic Potts Model in Three Dimensions: Universality and Critical Amplitudes // Phys. A: Stat. Mech. Its Appl. 1994. V. 210. Р. 217.
- Yamaguchi C., Okabe Y. Three-Dimensional Antiferromagnetic q -State Potts Models: Application of the Wang-Landau Algorithm // J. Phys. A.: Math. Gen. 2001. V. 34. Р. 8781.
- Zhang L.-R., Ding C., Deng Y., Zhang L. Surface Criticality of the Antiferromagnetic Potts Model // Phys. Rev. B. 2022. V. 105. Р. 224415.
- Wolff U. Collective Monte Carlo Updating for spin systems // Phys. Rev. Lett. 1989. V. 62. Р. 361.
- Swendsen R.H., Wang J.Sh. Nonuniversal critical dynamics in Monte Carlo simulations // Phys. Rev. Lett. 1987. V. 58. P. 86.
- Metropolis N., Rosenbluth W., Rosenbluth N., Teller A.H., Teller E. Equation of state calculations by fast computing machines // J. Chem. Phys. 1953. V. 21. P. 1087.
- 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. Р. 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. Р. 735–743.
- Бабаев А.Б., Муртазаев А.К. Моделирование трехкомпонентной модели Поттса на гексагональной решетке методом Монте-Карло // ФММ. 2023. Т. 124. С. 577–583.
- Ferrenberg A.M., Swendsen R.H. Optimized Monte Carlo data analysis // Phys. Rev. Lett. 1989. V. 63. Р. 1195.
- Муртазаев А.К., Бабаев А.Б. Вычислительная физика и проблемы фазовых переходов. М.: Физматлит, 2023. 184 с.
- Кузнецов А.В. Термодинамика. Екатеринбург: Урал. ун-т, 2023. 196 с.
- Bazavov A., Berg A.B., Dubey S. Phase Transition Properties of 3D Potts Models // Nuclear Physics B. 2008. V. 802. Р. 421–434.
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