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Year 2024, Volume: 8 Issue: 2, 243 - 250, 31.12.2024

Ali Tozar , Orkun Taşbozan , Ali Kurt

https://doi.org/10.38088/jise.1085180

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.

Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation

Year 2024, Volume: 8 Issue: 2, 243 - 250, 31.12.2024

Ali Tozar , Orkun Taşbozan , Ali Kurt

https://doi.org/10.38088/jise.1085180

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.
There are 13 citations in total.

Details

Primary Language English
Subjects Numerical Solution of Differential and Integral Equations
Journal Section Research Articles
Authors

Ali Tozar 0000-0003-3039-1834

Orkun Taşbozan 0000-0001-5003-6341

Ali Kurt 0000-0002-0617-6037

Early Pub Date December 16, 2024
Publication Date December 31, 2024
Published in Issue Year 2024 Volume: 8 Issue: 2

Cite

APA Tozar, A., Taşbozan, O., & Kurt, A. (2024). Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation. Journal of Innovative Science and Engineering, 8(2), 243-250. https://doi.org/10.38088/jise.1085180
AMA Tozar A, Taşbozan O, Kurt A. Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation. JISE. December 2024;8(2):243-250. doi:10.38088/jise.1085180
Chicago Tozar, Ali, Orkun Taşbozan, and Ali Kurt. “Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation”. Journal of Innovative Science and Engineering 8, no. 2 (December 2024): 243-50. https://doi.org/10.38088/jise.1085180.
EndNote Tozar A, Taşbozan O, Kurt A (December 1, 2024) Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation. Journal of Innovative Science and Engineering 8 2 243–250.
IEEE A. Tozar, O. Taşbozan, and A. Kurt, “Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation”, JISE, vol. 8, no. 2, pp. 243–250, 2024, doi: 10.38088/jise.1085180.
ISNAD Tozar, Ali et al. “Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation”. Journal of Innovative Science and Engineering 8/2 (December2024), 243-250. https://doi.org/10.38088/jise.1085180.
JAMA Tozar A, Taşbozan O, Kurt A. Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation. JISE. 2024;8:243–250.
MLA Tozar, Ali et al. “Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation”. Journal of Innovative Science and Engineering, vol. 8, no. 2, 2024, pp. 243-50, doi:10.38088/jise.1085180.
Vancouver Tozar A, Taşbozan O, Kurt A. Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation. JISE. 2024;8(2):243-50.
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