Abstract
The Heisenberg spin chain concept is a fundamental and generic model that describes the exotic magnetic behavior of certain materials, such as ferromagnetism, antiferromagnetism,
andferrimagnetism under critical temperatures. The concept of spin chain is based on Coulomb interactions due to Pauli exclusion principle rather than dipole-dipole interactions in explaining the high energy observed in the Weiss molecular field. With certain improvements to the Hamiltonian proposed by Heisenberg, the model has became more sophisticated and used successfully in explaining many of the physical phenomena observed experimentally. This model has been extensively studied by physicists since the emergence of quantum physics at the beginning of the 20th century. Due to nonlinear interactions inherent in the model, soliton solutions that can be obtained have attracted the attention of mathematicians, in recent decades. In this study, triangular soliton, bell shaped solitary wave and kink shaped solitary wave solutions were obtained by applying the functional variable method to the nonlinear Heisenberg spin chain equation for a cubic lattice crystal.
Keywords
Heisenberg Ferromagnetic Spin Chain Equation Analytical Solution. Functional Variable Method
References
- [1] H.A. Zad, N. Ananikian, Phase transitions and magnetization of the mixed-spin Ising- Heisenberg double sawtooth frustrated ladder, J. Phys.-Condes. Matter, 30 (2018) 9.
- [2] P.Weiss, L’hypoth`ese du champ mol´eculaire et la propri´et´e ferromagn´etique, J. Phys. Theor. Appl., 6 (1907) 661-690.
- [3] W. Heisenberg, Zur Theorie des Ferromagnetismus, Zeitschrift f¨ur Physik, 49 (1928) 619- 636.
- [4] H.Y. Zou, R. Yu, J.D. Wu, Universality of Heisenberg-Ising chain in external fields, J. Phys.-Condes. Matter, 32 (2020) 8.
- [5] H.A. Zad, N. Ananikian, R. Kenna, The specific heat and magnetic properties of two species of spin-1/2 ladders with butterfly-shaped unit blocks, J. Phys.-Condes. Matter, 31 (2019) 11.
- [6] H.A. Zad, M. Sabeti, A. Zoshki, N. Ananikian, Electrocaloric effect in the two spin-1/2 XXZ Heisenberg edge-shared tetrahedra and spin-1/2 XXZ Heisenberg octahedron with Dzyaloshinskii-Moriya interaction, J. Phys.-Condes. Matter, 31 (2019) 11.
- [7] D.V. Dmitriev, V.Y. Krivnov, Heisenberg-Ising delta-chain with bond alternation, J. Phys.- Condes. Matter, 30 (2018) 8.
- [8] T.A. Sulaiman, T. Akturk, H. Bulut, H.M.Baskonus, Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic Waves and Applications, 32 (2018) 1093-1105.
- [9] H. Triki, A.M.Wazwaz, New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, J Electromagn Waves Appl., 30 (2016) 788- 794.
- [10] T. Anitha, M.M. Latha, C.C. Vasanthi, Dromions in (2+1)-dimensional ferromagnetic spin chain with bilinear and biquadratic interactions, Physica A., 415 (2014) 105-115.
- [11] M. Inc, I.E. Inan, Y. Ugurlu, New applications of the functional variable method, Optik, 136 (2017) 374-381.
- [12] Y. Cenesiz, O. Tasbozan, A. Kurt, Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system, Tbilisi Mathematical Journal, 10 (2017) 118-126.
- [13] O. Tasbozan, N.M. Yagmurlu, A. Esen, The functional variable method for some nonlinear (2+ 1)-dimensional equations, Selcuk Journal of Applied Mathematics, 14 (2013) 37-46.
Abstract
References
- [1] H.A. Zad, N. Ananikian, Phase transitions and magnetization of the mixed-spin Ising- Heisenberg double sawtooth frustrated ladder, J. Phys.-Condes. Matter, 30 (2018) 9.
- [2] P.Weiss, L’hypoth`ese du champ mol´eculaire et la propri´et´e ferromagn´etique, J. Phys. Theor. Appl., 6 (1907) 661-690.
- [3] W. Heisenberg, Zur Theorie des Ferromagnetismus, Zeitschrift f¨ur Physik, 49 (1928) 619- 636.
- [4] H.Y. Zou, R. Yu, J.D. Wu, Universality of Heisenberg-Ising chain in external fields, J. Phys.-Condes. Matter, 32 (2020) 8.
- [5] H.A. Zad, N. Ananikian, R. Kenna, The specific heat and magnetic properties of two species of spin-1/2 ladders with butterfly-shaped unit blocks, J. Phys.-Condes. Matter, 31 (2019) 11.
- [6] H.A. Zad, M. Sabeti, A. Zoshki, N. Ananikian, Electrocaloric effect in the two spin-1/2 XXZ Heisenberg edge-shared tetrahedra and spin-1/2 XXZ Heisenberg octahedron with Dzyaloshinskii-Moriya interaction, J. Phys.-Condes. Matter, 31 (2019) 11.
- [7] D.V. Dmitriev, V.Y. Krivnov, Heisenberg-Ising delta-chain with bond alternation, J. Phys.- Condes. Matter, 30 (2018) 8.
- [8] T.A. Sulaiman, T. Akturk, H. Bulut, H.M.Baskonus, Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic Waves and Applications, 32 (2018) 1093-1105.
- [9] H. Triki, A.M.Wazwaz, New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, J Electromagn Waves Appl., 30 (2016) 788- 794.
- [10] T. Anitha, M.M. Latha, C.C. Vasanthi, Dromions in (2+1)-dimensional ferromagnetic spin chain with bilinear and biquadratic interactions, Physica A., 415 (2014) 105-115.
- [11] M. Inc, I.E. Inan, Y. Ugurlu, New applications of the functional variable method, Optik, 136 (2017) 374-381.
- [12] Y. Cenesiz, O. Tasbozan, A. Kurt, Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system, Tbilisi Mathematical Journal, 10 (2017) 118-126.
- [13] O. Tasbozan, N.M. Yagmurlu, A. Esen, The functional variable method for some nonlinear (2+ 1)-dimensional equations, Selcuk Journal of Applied Mathematics, 14 (2013) 37-46.
Details
| Primary Language | English |
|---|---|
| Subjects | Numerical Solution of Differential and Integral Equations |
| Journal Section | Research Articles |
| Authors | |
| Early Pub Date | December 16, 2024 |
| Publication Date | |
| Published in Issue | Year 2024Volume: 8 Issue: 2 |
Cite
The works published in Journal of Innovative Science and Engineering (JISE) are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.