Influence of the interaction on the heat capacity critical exponent for 1D Ising ferromagnet with periodical boundary conditions

Z.V. Dzyuba, V.N. Udodov, D.V. Spirin show affiliations and emails
Received: 21 April 2017; Revised: 04 August 2017; Accepted: 17 August 2017
This paper is written in Russian
Citation: Z.V. Dzyuba, V.N. Udodov, D.V. Spirin. Influence of the interaction on the heat capacity critical exponent for 1D Ising ferromagnet with periodical boundary conditions. Lett. Mater., 2017, 7(3) 303-306


The finite-dimensional scaling method was used to calculate the critical heat capacity index α. It is established that the growth of the energy parameters of the multi-spin interaction substantially affects the critical heat capacity index.In the framework of the spin flip dynamics algorithm with an original expression for the energy, an influence of the interaction of second, third neighbors, four-particle interaction, temperature and size of a 1D Ising ferromagnet on the heat capacity critical exponent is studied. Periodic border conditions are used. The critical index α is calculated by the finite size scaling method. It is established that the growth of energy parameters of the multi-spin interaction significantly affects the heat capacity exponent. Interaction energy of third neighbors decreases the value of α to a greater extent than the second-neighbor interaction J2 and four-particle one J1 – 4. Different characters of the influence of pair and four-particle interactions on α are revealed. Energy parameters are established for which this critical exponent attains negative values. For instance, taking into account the interaction energy of third neighbors, with an approach to the critical region, the heat capacity critical exponent has a minimum near negative value of α = –0.0043 ± 0.0005. With increasing number of nodes in the 1D Ising chain, heat capacity critical exponent increases. Extrapolation according to the inverse size of the system in the thermodynamic limit gives the values α = 0.19 ± 0.02, α = 0.17 ± 0.02, α = 0.20 ± 0.02, when one takes into account the interaction energy of second neighbors J2 = 0.1, third neighbors J3 = 0.1 and four-particle interaction J1 – 4 = 0.1, respectively. Note that the second neighbor and four-particle interaction energies do not change the sign of the critical exponent for N > 6, and when approaching the critical region the critical exponent α tends to zero. The results obtained are compared with the values for Ising model with "broken ends" boundary conditions, as well as with other known results for two-dimensional and three-dimensional cases.

References (13)

1. L. Bogani, W. Wernsdorfer. Nat. Mater. 7, 179 - 186 (2008).
2. H. Miyasaka, T. Nezu, K. Sugimoto, K. Sugiura, M. Yamashita, R. Clérac. Chemistry. 2005 Feb 18;11 (5):1592 - 602.
3. H. Miyasaka, M. Julve, M. Yamashita, and R. Clérac. Inorganic Chemistry 2009 48 (8), 3420 - 3437. Crossref
4. M. Yatoo, G. Cosquer, M. Morimoto, M. Irie, B. Breedlove, M. Yamashita. Magnetochemistry, 2016, 2, 2, 21. Crossref
5. C. Li, J. Sun, M. Yang, G. Sun, J. Guo, Y. Ma, and L. Li. Crystal Growth & Design 2016 16 (12), 7155 - 7162. Crossref
6. H. Gould, and J. Tobochnik. An Introduction to Computer Simulation Methods. Applications to Physical Systems. Part 2. Reading, MA: Addison-Wesley, (1988).
7. Zh. V. Dzuba, V. N. Udodov, D. V. Spirin. Fundamental problems of modern materials science, 2016, Volume 13, № 4, p. 430 - 436 (in Russian) [Дзюба Ж. В., Удодов В. Н., Спирин Д. В. Фундаментальные проблемы современного материаловедения, 2016, том 13, № 4, с. 430 - 436].
8. K. Binder, D. V. Heerman. Metody Monte-Karlo v statisticheskoj fizike: Vved. - M.: Nauka, 1995. - 141 p. (in Russian) [К. Биндер, Д. В. Хеерман. Методы Монте-Карло в статистической физике: Введ. - М.: Наука, 1995. - 141 с.].
9. L. D. Landau, E. M. Lifshitz. Course of Theoretical physicsCourse of Theoretical physics, Vol. 5: Statistical physics, Part I (Nauka, Moscow, 1995; Butterworth-Heinemann, Oxford, 2000).
10. M. Marinelli, F. Mercury, U. Zamit, R. Pizzoferrat, F. Scudieri. Phys. Rev. B49, 14, 9523 (1994).
11. A. G. Gamzatov, Sh. B. Abdulvagidov, A. M. Aliev, K. Sh. Khizriyev, A. B. Batdalov, O. V. Melnikov, O. Yu. Gorbenko, A. R. Kaul. Physics of the Solid State, 2007, Vol. 49, No. 9, p. 1686 - 1689 (in Russian) [А. Г. Гамзатов, Ш. Б. Абдулвагидов, А. М. Алиев, К. Ш. Хизриев, А. Б. Батдалов, О. В. Мельников, О. Ю. Горбенко, Кауль А. Р. Физика твердого тела, 2007, том 49, № 9, с. 1686 - 1689].
12. I. K. Kamilov, Kh.K Aliev. Phys. Usp. 40 639 - 669 (1983) (in Russian) [И. К. Камилов, Алиев Х. К. УФН 140 639 - 669 (1983)].
13. E. V. Shabunina, V. N Udodov, D. V. Spirin. Modeling of nonequilibrium systems: Proceedings of the XV All-Russian Seminar / Krasnoyarsk: Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences, 2012. - P. 231 - 234. (in Russian) [Е. В. Шабунина, В. Н. Удодов, Д. В. Спирин. Моделирование неравновесных систем: Материалы XV Всероссийского семинара / Красноярск: Институт вычислительного моделирования Сибирского отделения Российской академии наук, 2012. - С. 231 - 234.].

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